Here is a link to the tombstone for John. Note that this site and Ancestry suggest parents for his line, namely John Waite (1807-1851) and Jane Caldwell (1808 - 1891) as well as several potential siblings.
Here is the link for Jane Caldwell's grave where she is mentioned as John A.'s mother. It includes a supposed picture of Jane Caldwell. I find it odd that only John A. is mentioned as a child, and that her maiden name is used. The site also suggests she was married thrice.
On Ancestry, one member has detailed his tree with the same parents and included this picture. They suggested that John A.'s grandfather was Henry Wait (b. 1782) in Pittsburgh area.
I'd take all this information with a bit of skepticism, it is not documented fact. Some seems more probable than other. I always wonder when I see a PA connection if this is the German Wait/Wecht line. See the link in the other response I gave in this forum for more details. Didn't see Henry or John there, but could still be connected somehow.
If there is something more specific you are looking for, perhaps I can help more.