Green’s Dictionary of Slang

very, completely, used to describe drunkenness.

1910		Bulletin (Sydney) 27 Oct. 16/1: I never seen him loaded up like you or me or Snowy; / But, all the same, old Alfie D., gets rolling tight as Chloe.
1912		Bulletin (Sydney) 24 Oct. 16/2: On the second day of my stay, Ernest Spence, who was a Geordie miner, came home, rolling drunk, and the concern of his poor little wife touched my heart.
1944		L. Glassop We Were the Rats 55: A fat lot she’d care whether I was rolling drunk or not.
1958		A. Sillitoe Sat. Night and Sun. Morning 90: I don’t want to have you rolling drunk all over the place.