My problem with this hand is this:

A decent player would probably have a strong hand here. Probably. The problem is, an irrational player doesn't play the OPPOSITE of what a good player would do.

But unless you literally think he's pressing buttons at random, you have to ask yourself what hand makes a play like this? He either:

a) likes his hand pre/flop or on the flop, and is slowplaying it
b) he has hit on the turn
c) he thinks you're bluffing or weak

a) is possible - it's rather a decent line with aces heads up against a TAG. But you think he'd do this with AQ as well, I guess? b) is unlikely, though it adds another draw - would 34c raise here? The 6 is also a good set card for him, even if that's pretty unlikely. As for c), well, if he is a decent lagg then it's not a bad move on his part - but your whole argument is based on him NOT being a good lagg! Unless you know he's not a good lagg because you've seen him minraise turns and show down third pair - in which case we really need this read to be shared with us.

If he calls a lot pre-flop then he could have pretty much any hand that hit the board, from K2 to 66. But a bad player playing such an obvious two pair+ line probably DOES have 2 pair plus - this doesn't feel like a value situation, I dunno.

The ultimate problem is that whether he's played the hand well or badly, he's put you in a very tough spot. You're repping what you've got - he's telling you he has you beat. Most of the time, when a bad player does this, they're not lying.

(please note I have absolutely no idea how I'd have played this hand - quite possibly exactly the same way, because I'd be unable to lay down with such good odds against a craptard)