Not too sure about this....

What is the hand range of this villain to call a preflop raise?

Pot the flop... I'd probably go $4 on the turn.

That being said, the river call is pretty tough, in my opinion.

Hmm....

Does villain consider you tight? In my home game, many players will make these big moves on me knowing I'll lay down marginal hands. With AK, I'd definitely call those types of players.

If it's a more honest player, I'd probably lay it down. A big river bet after 2 calls is usually a strong hand, in my opinion. You showed strength twice, and he said OK.

The check may have enticed him to bluff, but he's -still- called twice.

Would this be considered a way-ahead, way-behind kind of hand from the turn?