He was born in Rotterdam, but he grew up in Thuringia, Germany.
When he was 18 years old, he sailed to America with his older brother, Johann Heinrich, and his wife and son, and his cousin, Johann Jacob Bach (FAG #169310220).
Copies of the passenger lists showing the names of these three men can be found here: passenger lists
The Americanized version of his name is John William Back, and so he became known as "John Back," or sometimes, "John Beck."
He married Mary Marberry (or Barberry), around 1759, and they had at least two children: John (born June 25, 1760) and Jacob (born March 9, 1764). Their son John was later known as John Back, and their son Jacob was later known as Jacob Back.
Johann Wilhelm and his family left Culpeper County around 1772, and they migrated to some land that was located along Copper Creek, in southwestern Virginia, right where it flows into the Clinch River. (It was then in Fincastle County. It soon became Washington County, and then it became Russell County, in 1786.)
On June 20, 1785, he bought 250 acres "on the waters of Copper Creek, a branch of the Clinch River." (Virginia Land Office Grants Q, 1785, p. 404 (Reel 57). He paid one pound, 5 shillings sterling. It had been surveyed on 5-10-1782.
On July 4, 1785, he bought 140 acres "on the forks of Copper Creek, a branch of the Clinch River adjoining Joshua Roman." (Virginia Land Office Grants R, 1785, P. 5 (Reel 58). He paid 15 shillings sterling. It had also been surveyed n 5-10-1782.
It is suspected that these two parcels were adjacent to each other. He had a total of 390 acres, with these two purchases. Sometime after that, and before 1792, he bought an additional 30 acres (probably along Moccasin Creek nearby). He was listed in the Land Tax Lists of Russell County as owning 420 acres.
After Johann Wilhelm died, in 1794, his widow was listed on the 1795 tax list in Russell County, VA as "Mary Marberry Back." That is how we know her name was Mary Marberry. (It is believed that she died, later in 1795, because she was no longer seen on any tax list there.)
After he died, two of his great nephews (Joseph Back Jr. and his brother John Back) went to his farm and helped his widow Mary settle the estate. She died soon after that.
Johann Wilhelm and his wife Mary were probably both buried on that farm.
His great nephew John Back married Catherine Robertson in 1795, who lived a short distance away, with her family. Since his great uncle's farm was then vacant, he and Catherine decided to live there. They ended up living there, until 1810, when they went to southeastern Kentucky.
UPDATE: The Library of Virginia maintains a card file with the historical records collected by Gordon Aronhime, in the area around the Holston-Clinch River, in the 1700s. There are two cards about John Back (now attached to this memorial). The cards refer to him as John Beck Sr., but his last name was first written as Back. It says that he moved to the Clinch River with his son, John Jr. (the man who served in the Rev. War). It shows that he lived on Copper Creek (later in Russell County). On Jan. 27, 1775, it looks like there was a letter from WP to AC, in which AC had engaged John to go to New Pines to see a salt peter mine (unreadable—in exchange?) with WP, for a powder mill with letter (unreadable) re powder mill. This was also in the Draper manuscripts. The card shows that his sons were John Jr., and Jacob, both of Virginia.(Both are linked here, on FAG.) On August 20, 1777, he administered the estate for Nathaniel Brown with Humphrey & Henry Dickenson, security was 50 pounds. On May 20, 1783, he donated one hog for use by the Washington County militia (unreadable) under command of Lt. John Berry. On June 27, 1794, he sold to John Harris a tract of 140 acres in the forks of Copper Creek, adjacent to Joshua Romans (Russell County). It appears that he had settled that land in 1775, and got ownership of it on May 10 1782. There appears to have been another 250 acres on Copper Creek, which he had settled in 1774, and he got ownership of it on May 6, 1782.