By the late 1800's to early 1900's Arkansas was on a route followed by several major or minor American Abernathy Lineages. The ones that went into the upper mid-west from VA after the Revolution, the ones that went to Missouri from several eastern states (VA, TN, NC, SC) after we bought all of then Louisiana from France, and the ones that moved across the deep South (AL, GA, MS & TX) from points east.
That gives you potential origins of VA, WV, KY, OH, IL, IN, MO, TN, NC, SC, GA, AL, MS, even TX. And some of those lineages were not, as far as we have been able to determine, at all related (in historical times) to the bulk of the other branches. Most of the early Tennesse branches that moved west to MO and KY derived initially from VA and the Carolinas; most of the ones in the upper mid-west from up-state VA (now WV) & PA who moved to MO were totally unrelated to the ones in the Carolinas or Tennessee; there was also a branch that ended up in MO & IL from an area of the UK along the border with Scotland, also probably unrelated to the ones from the earliest American Colonial times of VA and the New England States.
Do you have any dates on them at all? Not even years of death?
The ones on the 1900 Federal Census for Crittenden County, just east of present day Parkin in Cross County are all listed as Blacks. There are, as far as I've been able to determine, no listings for a Walter Abernathy or Abernethy on the our project's 1880, 1900, 1910, 1920, or 1930 Federal Arkansas census records.
Of the twenty Walter Abernathys in our Y-DNA project database, 6 were from NC, and one each from SC, GA, AL, MS, TX, VA, MO, KS, OH, or MT, and only a very few of those 20 could potentially be omitted, due to spouses, children, or deaths in county/state of birth.
More research on the spot in Cross County, Arkansas seems mandated.