I don't call anyone in my family by it, but I have heard it before. I'm not getting what is so creepy about "Big Daddy" either

. To a child, that is often the easiest explanation. It's better than "Old Daddy"

.
It's just a name for little ones to call the older folks, like Mee-Maw, Paw-Paw, Mimi, Papa, Pa, Pop, etc. But like those names, it just kind of becomes the name that everyone calls them, at least when talking to the children. It just catches on like any nickname.
Another common thing in the south, at least in some protestant denominations, is to call the church service "Big Church". To children, that distinguishes it from children's church (a service during church time that is more geared at children). It's the same general idea.