Hey, Bruce.I found your guy in the 1900 census for Gaston County, River Bend Township, Super. Dist. 8, Enumeration Dist. 82, Sheet 5.They really butchered the name but I am sure this is him although spelled ABBERNATHY:
Robt. L, Head, born Apr. 1864, married 15 years Florence, Wife, born Aug 1859, married 15 years Ella, Daughter, born Dec. 1886, single Rueben, Son, born Dec. 1889, single Oral, Son, born Dec. 1894, single Julian, Son, born Dec. 1897, single
All this ties in to an 1885 marriage and the census for 1880 shows Robt. was born in 1864.