Did not die in 1694 (an early error now corrected by scholars). Dr. Jonathan Avery of Dedham, son of Dr. William Aveary and Margaret Allright. "Jonathan Avery, third son of Dr. William and Margaret Avery, was born May 26, 1653, in Dedham, the first child born in their new American home. He became a physician, like his father." Married July 22, 1679, to Sybill Sparhawk (her first husband). Died September 14, 1690. Dr. Jonathan Avery was about 35 years old when he wrote his will. Earlier published records incorrectly state 1694 as year of death.

"1653 — Jonathan, the Son of William & Margarett Avery, was borne the 26th of the 3rd month."
— The Early Records of the Town of Dedham, Massachusetts
https://archive.org/details/earlyrecordsofto01dedh/page/6/mode/1up

Jonathan was born in Dedham, Massachusetts, May 26, 1653. Married July 22, 1679, Sybil Sparhawk, "born about 1655"; she was a daughter of Nathaniel and Patience (Newman) Sparhawk of Cambridge.

Jonathan died September 14, 1690, in Dedham, "inventory taken May 13, 1691", leaving four children. His widow Sybil (Sparhawk) Avery married second, Rev. Michael Wigglesworth, born October 13, 1631 (Harvard, 1651), "died June ye 10th, 1705" in Malden, Massachusetts, where a street perpetuates his memory. His widow died August 6, 1708.
— The Warren, Little, Lathrop, Park, Dix, Whitman, Fairchild, Platt, Wheeler, Lane, and Avery Pedigrees of Samuel Putnam Avery 1847-1920. Published by The New York Genealogical and Biographical Society.
https://babel.hathitrust.org/cgi/pt?id=wu.89062942289&view=1up&seq=263

Father of Margarett (infant), Sybil, Margarett (again), and Dorothy. Resident of Dedham, Suffolk County (today, Norfolk County), Massachusetts. Dr. Jonathan Avery died September 14, 1690. His will was recorded May 1690/91. (Old & new style dates may be muddled together - it appears he died in the fall and his will was processed the following spring.) Reverend Michael Wigglesworth visits Sybill the widow in October, the month immediately following Dr. Avery's death in September. Wigglesworth soon begins a formal courtship, and in 1691 he marries the widow Sybill (Sparhawk) Avery.

— Colonial Society of Massachusetts, Annual Meeting February 1912.
https://www.colonialsociety.org/node/285

Children of Dr. Jonathan Avery and Sybill Sparhawk
All were daughters. Their first child, a daughter Margarett, died as an infant. Second daughter Sybil Avery married Dr. Thomas Graves, had children, and has descendants. The third daughter, also named Margarett, died in 1694. Their fourth child, a daughter Dorothy, married Samuel Angier, had children, and has descendants (Samuel Angier was Dorothy's distant cousin, both being descendants of John Angier and Anna Sherman: Dorothy Avery, by her mother Sybill Sparhawk, was an Angier descendant).

Siblings of Dr. Jonathan Avery
Mary Avery Tisdale (born in England 1645; married 1666 in Dedham to James Tisdale, had children; died 1713 in Massachusetts); William Avery, deacon (born 1647 England; married 1st in 1673 to Mary Lane, 4 children; 2nd in 1683 to Elizabeth White, 5 children; 3rd in 1698 to Mehitable Hinkley, no children; died 1708 in Dedham); Robart Avery, ensign (born 1649 in England; married Elizabeth Lane, 6 children; died 1722 in Dedham); Jonathan, born 1653, married Sybill Sparhawk; Rachel Avery Sumner (born 1657 in Dedham, married 1677 to William Sumner, deacon, no children; died about 1678); Hannah Avery Dyar (born 1660 in Dedham; married 1677 to Benjamin Dyer of Dedham on the same day as sister Rachel was married, had no children; died 1678 in Dedham); "Ebenezer Avery, the youngest son and seventh child of Dr. William and Margaret Avery, was born Nov. 24, 1663. He must have died young, as he is not mentioned in his father's will, 1683."

Son of Dr. William Avery
William Avery, in Savage, James. A Genealogical Dictionary of the First Settlers of New England: Showing Three Generations of Those Who Came Before May, 1692, on the Basis of Farmer's Register. (Boston: Little, Brown, and Co, 1860-1862)
1:83. "William (Avery), Dedham, a physician, or apothecary, probably both, ar. co. 1654, had William, born about 1646; Mary; Robert, about 1649; Jonathan, 26 May 1653; Rachel; Hannah, 27 Sept. 1660; and Ebenezer, 24 November 1663, who probably died young, as he is not named in the will of his father which is dated 15 October 1683. William Avery was a lieutenant 1673, of the town's company, and freeman 1677; possibly the bookseller, mentioned by Thomas, in his History II. on page 411, certainly the representative for Springfield 1669, and he died at Boston 18 March 1687, aged about 65. His wife Margaret had died 28 September 1678. Of the daughters: Mary married 5 November 1666, James Tisdale; Rachel married 22 May 1676, William Sumner; and Hannah married the same day, Benjamin Dyer."

Sybill, widow of Dr. Jonathan Avery, was married in 1691 to the prominent Harvard College theologian, Reverend Michael Wigglesworth.

With his wife Sybill Sparhawk, Jonathan Avery was a direct ancestor of a well-known Lowell family line in Boston. Direct descendants of Dr. Jonathan Avery and Sybill Sparhawk include members of the prominent Russell and Lowell families of Massachusetts. John Lowell "Jack" Gardner (whose wife was founder and benefactress of The Isabella Stewart Gardner Museum in Boston, Massachusetts) was a direct descendant of Dr. Jonathan Avery and his wife Sibyll Sparhawk Avery Wigglesworth.

Sybill Sparhawk was a daughter of Nathaniel Sparhawk of Cambridge and Patience Newman, daughter of Reverend Samuel Newman, founder of Rehoboth, and his wife Sibell Featley.

Some sites incorrectly claim Jonathan Avery died 1694. "Genealogy of The Sparhawk Family" provides the correct date, estimating 1690 the year Dr. Jonathan Avery died.

"Sibley's Harvard Graduates" shares this information, which further conclusively demonstrates Dr. Jonathan Avery died before 1691: "In the New England Historical and Genealogical Register, xvii. 139-142, are two letters written to her by Wigglesworth before their marriage. In the first, dated II February, 1690-1, wherein he makes known his purpose, he writes: "If you cannot conveniently return an answer in writing so speedily, you may trust the Messenger to bring it by word of mouth, who is grave & faithful, and knows upon what errant he is sent." After he had made her a visit, he writes another letter, 23 March, proposing still another visit, and sends ten "Considerations," drawn up in sermon style, which, he says, "Possibly may help to clear up yo' way before y° return an answer unto y* Motion w** I have made to you, I hope you will take them in good Part, and Ponder them seriously.""

Wigglesworth, quite simply, would not have proposed to a married lady. Therefore we can conclude 1690 is the accurate date of Avery's death. Wigglesworth begins his courtship of Sybill after he learns Dr. Jonathan Avery has died.

Jonathan Aurey and Sibbele Sparhauke marryed 22d, 5: 1679 (Married Sybil Sparhawk July 22, 1679).

From the records of the Colonial Society of Massachusetts, February 1912 meeting:
"26. The Avery mentioned by Mr. Lee is, beyond a doubt, Dr. William Avery of Dedham and Boston. He was admitted a townsman of Dedham in 1651, and, on February 16, he and his wife were received into the First Church there. In March he got permission to set up his smith's shop.

This agrees with Lee's remark that the Avery to whom he refers had formerly practised the "ars veterinaria,"i. e. farriery. William Avery's name occurs frequently in the records of Dedham, often with the title of Sergeant. In 1609 he was Deputy to the General Court. In 1673 he was appointed Lieutenant of the Dedham Military Company. In 1675 his name appears in the records with the title of "Mr.;" so also in 1679.

When he began to practise medicine we do not know; but his name bears the title "Doc" in the town records for 1676, and thereafter Doc, Do, or Doct is its common prefix.

On January 1, 1678, he obtained permission "to fell timber of the town common, for a frame of a house to carry to Boston, provided he paid to the use of the town in money two shillings per ton, not exceeding seven ton." This gives us an approximate date for his removal to Boston. In 1680 he offered the town of Dedham £60 for the encouragement of a Latin School, and in the same year there is the following important entry in the records of that town:
Capt Dan Fisher make a return of the trust Com̄ited to him selfe and En Tho Fullar of a Some of mony of sixty pounds giuen to the Towne and the Improument for the benifit of a Latine Schoole

The returne is as foloweth be it Here by declared that I Will Auery Phisision now resedent in Boston: some times of the Church of Dedham do out of my Intire loue to the: Church and Towne: thier frely giue the full Some of sixty pound in mony thier of to be wholy for the incoragmt of a latin Schoole as shall be from time to tim so ordered by the Elders or Elder of that Church and select men for the time being desirous yt others whom god shall make able will adde thier vnto that a latine Schoole may generaly be maintayned thier and this to stand vpon record in thier towne Booke.

In March, 1681, there is a further record about Dr. Avery's benefaction, as follows: — "it being proposed to the Town whether they will allow twenty two pounds by the year to a lattin schoolmaster whereof seaven pounds shall be mony besides the incom of that 60 pounds given by Docter Avery, it was voated in the afirmitive."

 And there are other entries relating to this same gift.

Mr. Lee says that "Dr Avery was a great inquirer and had skill in Helmont & chemicall physiek." By a lucky chance, two letters that show his inquiring mind and his addiction to chemistry are preserved in the Works of the famous natural philosopher, Robert Boyle, to whom they were addressed.

They are dated at Boston, November 9, 1682, and May 1, 1684. From them it appears that he was in hot pursuit of the alkahest or universal solvent. He refers to Starkey's Pyrotechny, and mentions "the worshipful Mr. Dudley and "my worthy friend Mr. Thomas Brattle."

In the second letter he speaks of a son "about thirty years of age" as also a "practitioner in physic, and an assiduous labourer at the chemical fire." This son was Jonathan Avery, of Dedham, who first appears in the town records in 1681 (with the title of Doctor), and often thereafter.

 Under date-of December 16, 1701, are mentioned "the Heires of Jonath Avery Deceased."

Dr. William Avery died in Boston, March 18, 1687. His will is preserved in the Suffolk County Probate Files, No. 1526. The testator describes himself as "resident in Boston," as "practitioner in physiek," and as "aged about 61 years." This was in 1683, for the will is dated on the 15th of October in that year. It is signed William Avery, and has two witnesses. Below their signatures is the acknowledgment in the presence of three witnesses, dated March 13, 1686–7. The will mentions the doctor's wife (Mary), and his four children, William, Robert, and Jonathan Avery, and Mary Tisdale; also his sons-in-law, William Sumner and Benjamin Dyer. There is an interesting bequest to charity which shows that the Doctor was interested in mines, as befitted a loyal student of alchemy:
Jt. Concerning my part in several mines, my Will is, that after all necessary charges already laid out or to be laid out upon them be equally satisfyed, then the profit or income of them while my wife lives, shall be divided to her & to my four children William, Robert & Jonathan Avery & Mary Tisdale, & after my Wife's decease shall be divided among my said children: And my will is that in all these divisions my son william shall have a double share . . . Further my [Will] is that a third part of all the profit yt shall arise to any & all of my children from the said mines shall be improved for publick & charitable uses according to their own discretion. And my will is that it shall so remain from time to time with them their heirs or successors, that, all necessary charges deducted, a third part of the profit of ye mines aforesaid shall be for publick & charitable use.

All medical books and apparatus are bequeathed to the Doctor's son Jonathan. "Jt. My Will is yt my son Jonathan shall have my two Stills, all my Physiek books & instruments, he allowing twenty pound to my executors for ye same." The three sons are named as executors, but on May 26, 1687, they filed a document renouncing their executorship. This, with the will, is all that the Suffolk Files contain. The will is docketed as taken to the Probate Office by William and Robert Avery on May 26, 1687.

The will of Dr. Jonathan Avery is also in the Suffolk Probate Files, No. 1856. He describes himself as "Jonathan Avery, resident in Dedham . . . Practitioner in Physiek, & aged about Thirty-five years." The will is dated February 18, 1689, and was recorded in May, 1691. The inventory, which is the only other document in the Files, is dated May 13, 1691, and was sworn to on May 27. The will mentions the Doctor's wife Sibyll, and his three daughters, Sibyll, Margarett, and Dorothy, all under age. His brother, William Avery, is also mentioned. The inventory values his "Bookes Devinitie & Pisicall & other small books" at £5, and his "Chyrurgion Jnstruments" at £1.
— Colonial Society of Massachusetts, Annual Meeting, February 1912.
https://www.colonialsociety.org/node/285

Further References:
Carter, Jane G. Avery (Jane Greenough Avery), and Susie P. (Susan Perry) Holmes. Genealogical Record of the Dedham Branch of the Avery Family in America. (Plymouth, Mass.: Winslow W. Avery, 1893), pages 85-97.
"Jonathan Avery, third son of Dr. William and Margaret Avery, was born May 26, 1653, in Dedham, the first child born in their new American home. He became a physician, like his father."

Jonathan Avery, in Savage, James. A Genealogical Dictionary of the First Settlers of New England: Showing Three Generations of Those Who Came Before May, 1692, on the Basis of Farmer's Register. (Boston: Little, Brown, and Co, 1860-1862)
1:82.
"Jonathan (Avery), Dedham, son of William, married 22 July 1679, Sybil, daughter of the second Nathaniel Sparhawk of Cambridge, had Margaret, born 9 November 1681, died young; Sybil, 11 August 1683; Margaret, again, 20 August 1686; and Dorothy, 4 July 1688; and he died 16 September 1694 [sic]. His widow married Rev. Michael Wigglesworth.
[Note: this date of death is incorrect, see NEHGR source cited, as well as remarriage of widow.]"

Hill, Don Gleason, Editor. The Record of Baptisms, Marriages and Deaths, and Admissions to the Church and Dismassals Therefrom: Transcribed from the Church Records of the Town of Dedham, Massachusetts, 1638-1845. Also all the Epitaphs in the Ancient Burial Place in Dedham, Together with the Other Inscriptions before 1845 in the Three Parish Cemeteries. (Dedham, Mass.: Town of Dedham, 1888), page 6.
"1653 … Jonathan, the Son of William & Margarett Avery, was borne the 26 of the 3 mo."
https://archive.org/details/earlyrecordsofto01dedh/page/6/mode/1up

Hill, Don Gleason, Editor. The Record of Baptisms, Marriages and Deaths, and Admissions to the Church and Dismassals Therefrom: Transcribed from the Church Records of the Town of Dedham, Massachusetts, 1638-1845. Also all the Epitaphs in the Ancient Burial Place in Dedham, Together with the Other Inscriptions before 1845 in the Three Parish Cemeteries. (Dedham, Mass.: Town of Dedham, 1888), page 25.
"Jonathan Avery, deceased September 14, 1694 [sic].
[Note: this date of death is incorrect, see NEHGR source cited, as well as remarriage of widow.]"

Stansell, Maxine. The Middlebrook Sisters: Mother and Mother-in-law of Michael Wigglesworth. New England Historical and Genealogical Register. (New England Historic Genealogical Society, Oct 2002)
156:318.
"Rev. Michael Wigglesworth … married third at the First Church in Braintree, Massachusetts, 23 June 1691, Sybil (Sparhawk) Avery, of Dedham, Massachusetts, … daughter of Nathaniel 2nd and Patience (Newman) Sparhawk, and widow of Dr. Jonathan Avery."

"Savage's Genealogical Dictionary, Corrections and Additions: Avery and Wilgglesworth", in The New England Historical and Genealogical Register. (Boston: New England Historic Genealogical Society) Volume 45, page 168.
"Will of "Jona. Avery Practitioner in Physic & aged about thirty-three" dated 18 February 1689, proved 27 May 1691. Also refers to Volume 17, page 139 where Michael Wigglesworth writes a letter dated 11 February 1690[/91] to Mrs. Avery, referring to her as a widow, and mentioning visiting last October (1690), presumably when he learned of her widowhood. Regarding the Dedham record [incorrectly stating this Dr. Jonathan Avery died in 1694]: "unless there be an error in the year, a different person must be intended."

Spelling variations for various relevant names include:
Aveary, Avery
Jonathan, John
Sybill, Sibell, Sybel, Sybil (other spellings possible)
Sparhawk, Sparhawke, Sparrowhawk, Sparrowhawke
Graves, Greaves
Robart, Robert
Margarett, Margaret
Angier, Anger

Died 1689/90 not 1694.