>I must be in Abernathy/Abernethy country in North Carolina.
You certainly are!
>If you put the name in search of early US Census, you will find them only in Virginia and North Carolina.
Well, not exactly. And depends on how you define "early" census, too.
1790: NC, SC
1800: CT, KY, NY, NC, OH, PA, SC, TN, VT
1810: CT, DE, KY, MD, NC, NY, PA, SC, VT, VA
1820: CT, IL, IN, KY, MD, MA, NC, NJ, OH, PA, SC, TN, VA
1830: AL, CT, GA, IL, IN, KY, MD, MO, NC, NY, OH, PA, SC, TN, VA, VT
1840: AL, CT, GA, IA, IL, IN, KY, MD, MI, MO, MS, NC, NJ, NY, OH, PA, SC, TN, VA, VT
You may note that CT, KY, and PA were as regular as NC & SC, once those states first appeared. Ohio and Tennessee are both missing from 1810, but otherwise well represented from 1800 on. West VA of course, is lumped in with VA from 1810 to 1860, inclusive.
Not all of the pre-1850 census years are particularly valuable, but 1830 and 1840 can be potentially more informative than earlier ones, due to a more precise division of age groups. The earlier ones? Well, not much. And in states and counties where the absence of early census records are missing, extant Deeds and Tax Records can be informative, but tedious. So many don't bother much with them.