Abig.

Abig. is a clerk's shortening of the given name Abigail. Busy writers cut common first names down to a few letters, often raising the last letters above the line, and the habit runs through deeds, wills, tax lists and census pages.

Abigail was a well-used Bible name in early America, and Abig. turns up in town, church and probate records. When an index shows a woman named Abig, look at the image: the transcriber may simply have kept the shortened form.