The sample size for turn play is obviously going to be a bit weird, but it looks a lot like he likes making moves on the turn. Given your history, and that he's limp/folded a couple of times on the button earlier, you also have to up the likelyhood of him doing this with a weaker hand than average. I don't think you can fold two pair anywhere, since the only thing you're really worried about is a wheel and a set, and there's quite a few combos of top pair he might convince himself is good on this turn.
So how do we get the money in?
I doubt that this is air. Naked bluffs shouldn't be in his range too often, even if he is getting sick of you. They tend to fight back preflop or on the flop when they wanna do the **** you-raise. And flushdraws don't play like this very often either, since the people who are capable of raising flush draws prefer to do it on the flop. Once he just calls the flop, he's calling again with the flush draw, hoping to stack you on the river.
So that leaves a gazillion different overpairs and jacks, 8 combos of sets, and 16 combos of wheels, if we think A2 is in his range, and I'd say that it is.
I just ship it in and shrug it off when it's the wheel. Sets are very rare, given that his second most probable set (combinatorically) is JJ, and I'd expect him to raise preflop with that most of the time, leaving really only 33 to make sense of the sets, and a wheel is five times as likely as 33, so...
Yeah, if he has a hand that beats us, it's the straight. At least we have four outs to the nuts when we shove and he snap calls us, then.
I don't see another way of playing it. I don't think I like calling, because what are we going to do on the river? Check to induce and let him get away cheaply with his AJ? Check/raise if he bets small? Donk? What do we do if a club rolls off? Or a deuce? Etc. He has position, and I'd really like to end that advantage for him immediately.
If we shove and he folds, we'll hate life for not letting him bluff the river, but really... What hand is he going to bluff the river with after we call a massive raise on the turn? He'd have to have churchbell-sized stones to bet the river after being called on the turn.
Summary: I like shoving the turn after he raises.