I like your pre-flop raise, building the pot in position against a weak range with AQ, could even size up against someone limping a very wide range to 280-320ish.
On the flop a c-bet can be very effective in making him fold hands like T9o or 87 that have decent equity and will fold for a small bet. I don't think any pair ever folds to a flop bet. Therefore I would c-bet around 1/3 pot on this dry texture. Betting full pot doesn't accomplish much, better hands will always call and worse will fold.
As played I don't think villain is ever check raising your pot sized c-bet as a bluff on this board. So I would fold flop in your situation. Had you c-bet 175 into 530 on the flop and he check-raised small you could float as AQ high is near the top of your range.