[rikz]

Given his small raise, and subsequent call to your very large reraise (rather than going all-in on you like he might with AA, KK, or often QQ), my guess is he has 88, 99, TT, JJ, or even AXs hearts where X is K, Q, J or T. All of those are possible reraising hands that wouldn't go all-in to your very large 3-bet preflop. I don't know why he'd min-raise you preflop with any hand that makes a straight or a straight draw on this board, so while that kind of hand is possible, I think it is highly unlikely (i.e. 4h6h...). I also think a low pocket pair to make a set is unlikely, albeit more likely than the straight because I have seen some players min-raise preflop with hands like 77 or 55.

So, even though you are a bit of a favorite over the AX hearts where X is T, J or Q, I agree with you that you're better off folding since you lose to the most likely hands (mid-sized pocket pairs), you lose to less likely sets, and you lose to very unlikely straights. You tie AK, but Ah has a back door flush advantage and AhKh has a nut flush draw. You are really only ahead of AX flush draws other than AKs.

To improve over the non-set/non-straight hands, your odds of hitting the A or K, asssuming villain doesn't have one already, is 7.3:1 against on the turn card and then 7.2:1 against on the river. These kind of odds make just calling a pretty bad option.

Finally, if you think he might be stone cold bluffing a missed AQo/AJo, then you would have to raise a huge portion of your stack to pay for that kind of information on the flop. A raise for information here might be a good idea with a smaller pot or bigger stacks against a habitual bluffer. Given this hand, however, that would cost you just about all your chips if your read is wrong about this being a bluff.