I am thinking about this hand, and I am having a tough time thinking of what would bet this way. Obviously not 3A of hearts since you got the hearts, so the pair and flush draw is out the door. He might have TJ or JQ of hearts, and playing his flush draw+gutshot hard. He could have AK, QK, JK, TK, or 9K, and only one of those hands you are behind, the rest you are ahead and one you tie. Or, he could have 33, 99, or QQ (check raising with the QQ to see if he is ahead or behind I guess), or he might be trapping with AA (I've seen this kind of thing before).

I am perplexed, my guess is most likely has 33, 99, or AK as aggressively as he is playing it.

According to pokertracker, you are 69% fave against this range. I would end up reraising all in right here since the flush didn't come, AK looks pretty good right here, and if you lose to a set, ouch.