I always thought "baby" was a Southern thing - finding out I'm wrong!
The sweetest little lady called me, "Baby" at a drive in window the other day. Made me smile - didn't mind at all.
Around here we use it to mean the same as "Honey, "Sweetie" - that sort of thing.
My husband's grandmother was from S. Texas (where we live now), but raised her family in OK. My MIL was so insulted when her mother called her "Baby" as a child. She took it to mean she was acting like a baby and was being corrected. When I called one of my kids "baby" when he was certainly too old for that to be true she cried. Decided she had it wrong all those years - that her mother had not been insulting her - just speaking Texan instead.
So .. people are babies around here. We have two pets that my husband treats as people, but to me people are babies, pets are pets.