I just transcribed the library of congress recording Lomax did of Ledbetter, where they discuss "tight like that". it was in reference to dancing:

Lomax: What does that mean by that, Huddie, really I mean tell us confidentially what that means by “Tight Like That”?
        Huddie Ledbetter: “Tight Like That” it means when you got your partner grab her and hug her tight, and keep it going, but when he sometimes a boy grab his partner and grab her and giving a hug he says, “tight like this.” It was tight like this but it’s not as tight like this and the boy’d be jumping on “Tight Like That”.