From the censuses, he appears to be the son of Marion Blanton, who was the son of John W. and Catherine (Munkers) Blanton. The lineage goes:

William and Hannah (Hobbs) Blanton of Lee County, Virginia>John and Elizabeth Blanton, who migrated to Missouri>Joseph Blanton, who died on the trail to Oregon>John W. and Catherine (Shephard) Blanton.

They are members of the family we call the Southwest Virginia Blantons. There are a number of bogus genealogies on the web which purport to connect William to the Caroline, Virginia, Blantons (Tidewater Blantons). However, there is no evidence for such a connection.

There is more information on this line in various posts on Genforum. Contact me directly at rbsgenealogy@ameritech.net and I will send you Louise McDonald's research on this family. It was not included in the Ramey book (downloadable at the Blanton Family Historians site).