I meant to caution you not to believe everything you find in the many on-line databases, but to verify them when possible. That was why I gave you source clues. Some of the Abernathy data has been copied without any attempt to verify it, and as a result there are several serious errors that even the most careful of researcher haven't been able to get corrected.
There is, for example, no evidence whatever that Mary, wife of the 3rd Robert was a Harwell before her marriage: the best of the Harwell researchers have been trying in vain for YEARS to find her and none have succeeded yet. And there is still the question of the 2nd Robert's wife's maiden name: was it Tilman or Parham? Her mother's will doesn't indicate the sequence of her children of her two marriages, so we have no clue.
Also, none of the earlier Roberts had a middle initial until about 1932 when journalistic constraints by a small-town Tennessee newspaper forced Elizabeth Denty Abernathy to use "A." for "Abernathy" thus saving 7 spaces every time it appeared in the column. Which was often. There are other known errors in many on-line databases, one of which being the theoritical link back to the Scottish Aristocracy. It was disproved about a century ago by THE pre-eminent authority on Scots genealogy, but persists until this day. In spite of everything. Understandable: it's a fine, warm, fuzzy feeling to think you're descended from Royalty. Even when you're not. I know: it beguiled me for the better part of 10 years. Until I learned enough to understand why it wasn't so...
What we do know and can prove is Robert Abernathy's arrival on these shores. What we can't prove is who his parents were back in the old country. And a costly dead end it proved to be, too, since certified Scottish and British genealogists don't exactly come cheap. But at that, it's further back than many can go: I've got one line that is a dead end at 1818, unlike the Virginia Abernathy lineage that begins on these shores in the spring of 1652 with an illiterate indentured bondsman who was a survivor.