Well, my guess (from the year and place) is that this is from old Redmond Fallin's family
Redmond Fallin (Falling, Faulling, Fallin, Faullin, Fallon etc etc). was a long hunter and had started having lands surveyed around 1745 or 1747 in Pittsylvania county (near or in Danville, Virginia) by the sandy creek of the dan river.
I'm doing this from memory, but I'm thinking William was one of his sons.I am a direct descendant of this family via the Redmond-Edmond-Redmond-Littlebury-Edward ...lines of this Fallin (Faullin-g etc etc) family
route was Virginia (possibly Maryland before Virginia) to Tennessee to Arkansas to Missouri to California and now I'm in New Mexico and married to a Mexican national... I call my kids my little "confederados"ha ha
Just google Redmond Fallin and/or Darby Fallin for more information