There's the will of George Cooper of Great Glen, gentleman, who died in 1798; his gravestone suggests that he was 81 years old. His will names the following:
His son George Cooper - executor
Another son Edward Cooper
Granddaughter Lidea Mary Folwell
Daughter Mary Thornton and her 4 children (unnamed, all under 21)
Grandson George Cooper, the son of George
The 1831 will of George Cooper the Elder, Great Glen,Gentleman, names the following:
Oldest son George Cooper - executor
Youngest son William Cooper (not yet 21 at the time of writing, which was 1825)
Wife Mary Cooper
The 1855 will of George Cooper, gentleman of Great Glen,has the following family members:
Sisters Mary Harrison (wife of John Harrison) and Eliza Coleman
Brother in law Henry Freeman Coleman
Brother William Cooper
He also mentions various friends, a minister, servants; and the children of Mary, Eliza and William, but doesn't name the children.
This was the most verbiose of these wills and I found the most difficult to read; I hope I haven't omitted anyone important.
So this all hangs together nicely with all the findings above.
Of particular interest re your William is the fact that he was under 21 in 1825, so he can't have been the 1799 baptism that you found.