Well, it appears that the 1771 will in NYC is from John Weems, married to Isabella Scott of Bucks Co., PA. I have also found John Weems, owning 100 acres in Abington, PA in 1734, which means that this is their earliest place of residence, which is where Thomas Scott Weems, born. 1704 would have been from.
It also appears that Alexander Wemyss of NYC is Thomas Scott Weems's brother. He died in 1782 and would have been born about 1710. There are undoubtebly other brothers and sisters, just need to find them. :-) Abington, PA will give us a new place to start.
I believe that Alexander Wemyss is the father of John Alexander Weems, b. 1745 of Greene Co., TN, meaning that the Greene Co., TN Weems and the Abbeville, SC Weems are first cousins. Still trying to find the will of Alexander in 1782, but it wasn't in the Surrogate Court of NY, but probably in the county somewhere. Still looking!
This also provides for a direct line back to the royal lines. Just need to fill in the blanks now! If anyone has any supporting information or odds and ends that just didn't fit anywhere else, please let me know. It might prove helpful in the end.