AQ vs. 4bet pre flop

Hero in a live $2/$5. Action folds to villain in cutoff pre flop and he raises the standard amount of 3xbb, I 3bet villain on button with AQ. Both blinds fold, and villain puts out a 4bet. Hero had been at table for ~1 hour, and had not seen villain put out a 4 bet pre flop. He had been 3bet a few times pre flop (mostly by hero) and he just folded, however the positions we were in we're earlier positions. I'm not sure if this note helps or if both factors cancel each other out. Facing the 4bet, I was getting 30% on the call. In retrospect, I should have called and not shoved because I wasn't a favorite against his range (villain 4bet with top 7% hands in my estimation and according to pokercruncher I was a 47%-53% underdog against his range). At the table, I wasn't sure how to maneuver post flop with so little behind, so I shoved instead of folded because I thought I was at the very worst, I was 45-55%, which was too tight for a fold, and there was enough in his 4betting range that would fold to a 5bet shove. Do you agree? Thanks for your help