From Genforum.com post:
Nathaniel Burwell, baptized 14 Oct. 1680 (Abingdon Register) succeeded his father at Fairfield. He died between 20 Aug and 14 Oct. 1721. His tombstone is extant at Abingdon Church, Gloucester County, and states: Major Nathaniel Burwell, Eldest son of Major Lewis Burwell ... died in the forty & first year of his age leaving behind him 3 sons and one daughter by Elizabeth, eldest daughter of Robert Carter, Esq.
The Fairfield or Carter's Creek estate descended to their son Lewis Burwell (1710-1752), president of the Governor's Council.