[pauliewalnuts]

Nobody has mentioned the percentage of times he has AA-QQ and 3bets you. Also, even if he has AK, he is likely to call your turn raise and then fold the river UI if you fire again(if he is the type that can fold AK on a rag board). So, in that case it would leave you in an uncomfortable spot on the river. If you miss, the only way you can win is to bet, but a lot of times he has just resorted to calling you down and you are wasting a bet since he wont fold.

So, Id just call. You've got a ton of outs. Wait until you hit one to put in multiple bets.