Thank you for that, it looks like you have solved the problem.
the other major problem now is finding out who was the grandfather of Thomas Burn 1748, and John Burn 1750 a Gainford, their father john had at least one brother and sister Anthony & Elizabeth, it would have been so nice to get into the 17th century.
I think it is possible that Anthony never married, as he left no money to a wife or children, perhaps they died?
Elizabeth married Thomas Watson they lived at Westerton, Durham, as did Anthony when he made out the will.
He also had another brother -in -law George Gilling.
John.