Green’s Dictionary of Slang

(orig. US) vaguely or unsteadily.

1917		D.G. Phillips Susan Lenox I 395: He caught them each by an arm, stared woozily at Etta.
1929		(con. 1917–18) C. MacArthur War Bugs 280: The lieutenant wabbled in, pointing his gun woozily.
1999		Indep. on Sun. Culture 12 Sept. 4: The often tepid mod-isms of Britpop reflecting today’s woozily nostalgic consensus.