Pretty consistant tithables on "William Carroll" from 1782 up to 1816 in Loudoun county (thanks Pat for lookup). Someone who has more time researching family could probably determine if this is the "William Porter Carroll".

Two sons appear:

Jesse (b. ABT 1775) based on 1792-1896 tithables of 16yrs of age
Enoch (b. ABT 1780) based on 1797-1800 tithables of 16 yrs of age

found oddball charater out in Grayson, Kentucky:
Elias K. Porter (b 1785-1862)with parents "William Porter" and "Ann Murphy Porter"