A loving, sweet term of endearment from a man to an attractive, cute, sexy, young looking "child woman." Perhaps influenced by the 1956 film Baby Doll where a much older man marries a girl simply named Babydoll who is on the cusp of childhood and womanhood or appears that way.
Meredith often calls his Child-Woman girlfriend Regan "his Babydoll." Regan looks very young looking for her age looking like a beautiful, porcelain doll. "Don't worry 'bout a thing, Babydoll."
This term is used to describe the location in which two secretive (or not entirely open) lovers may have disappeared to from any public setting/location. Although the definition is not meant to be literal, it is meant to suggest sexual bonds between the two lovers in question.
Dude 1: "Hey man, have you seen Bob?"
Dude 2: "Yeah, actually I just saw him with Karen a second ago... not sure where they are now."
Dude 1: "Oh! You know what that means: BABJ! I knew they were seeing each other!"