The villain is a 33/20 with >10 3Bet%. Not sure about pre-flop 4 bet, because 2/3 of time AK doesn't hit.
I prefer to call the 3 bet if the villain will fold hands like AQ/AJ. If you think he would call the 4bet with those kinds of hands, then 4 betting is ok.
Well played, you can shove on some boards even if you don't hit.
Wp, I like your line. 4 betting will also slow the villain in the future.