Holly, I hope you get this reply after so long. I am a descendent of Archibald Mattison, and the Bigbys are cousins that I am just getting to in my research.
I am confident that the grandson Archibald in the 1880 census is the son of John William and Catherine Bigby. Alice certainly is. She is with them in the 1870 census. I have been unable to find JW, Catherine, or their daughter Martha anywhere in the 1880 census. I assume that they went to Texas soon after the 1870 census and died there.
The only other plausible parent for young Archibald is "B. Bigbie 33 GA widow farmer" in Lamar TX with his 8-yr old daughter in the 1880 census. However, it is unlikely that a person in that situation would have kept his daughter with him and sent his 9-yr old son back to GA.