At this time, my research has only been able to prove that William Arthur lived and died in Bedford County, Virginia. Documentation found proves that he married Ann Watts in September of 1782.
The only child I have proven to be theirs is William Arthur, Jr. born in 1796.
There seem to be several William Arthur's in this time frame in Bedford County. Others claim to have only a daughter, and many different wives. Research is on-going.
Marriage Records
William and Anna's listing is the first one under the double line - "Virginia, County Marriage Records, 1771-1989," database with images, FamilySearch (https://familysearch.org/ark:/61903/3:1:3Q9MC9BK-RQ9M-1?cc=2134304 : 15 March 2021), > image 1 of 1; Accomat county court clerk offices, Virginia.
The entry for William Arthur and Anne Watts is third from the bottom. Source: Deed books, 1754-1901; general indexes, 1754-1929; Virginia County Court, Deed Book 7, page 343. Familysearch.org; film# 007846223. URL: https://www.familysearch.org/search/catalog/281939?availability=Family%20History%20Library
Sources:
"Virginia, County Marriage Records, 1771-1989," database with images, FamilySearch (https://familysearch.org/ark:/61903/3:1:3Q9MC9BK-RQ9M-1?cc=2134304 : 15 March 2021), > image 1 of 1; Accomat county court clerk offices, Virginia.
Deed books, 1754-1901; general indexes, 1754-1929; Virginia County Court, Deed Book 7, page 343. Familysearch.org; film# 007846223. URL: https://www.familysearch.org/search/catalog/281939?availability=Family%20History%20Library