[ArtVandelay]

My first bit of advice is don't raise AK pre-flop if you're getting in trouble with it after the flop. Unless your raise gets enough money in that you're pot committed (and I doubt this unless the stacks are really short), you should just call pre-flop. If he really is loose-aggressive you can probably get it all in when you actually flop a hand whether or not there was a raise pre-flop, so there's no reason to waste the money pre-flop for those times when you miss. Note that I only recommend this play when you're just starting out or when you're against a player who will outplay you when you miss the flop. The thing is, if he's pushing in way too much money when the flop comes rags, you'll crush him the times you actually have an overpair, so it's not so bad to always give up slick if you miss the flop. One of the things I rapidly learned about big bet Hold'em is that pre-flop just doesn't matter that much, unless the stacks are short (like in a tournament). AK is only a great hand pre-flop if you can get all the money in, and otherwise it's not much better than JT; both can hit the flop hard, but usually both make nothing. The key thing is, that unlike limit flopping a pair with AK doesn't mean you go to showdown 90% of the time. You'll often have to fold even when you flop your TPTK, or you'll win a small pot. Finally, at the higher levels you simply must raise non big pairs pre-flop or your opponents will know too much about your hand, but at the levels you're playing the deception value may not even be worth it. When you're against the loose-aggresive maniac just raise the big pairs, and call behind with everything else hoping to flop a big hand.

To answer your specific question, probably check behind and hope to make a pair on the turn. Of course, if you think he'll just give up half the time then you have an easy bet, but from the way you describe him it sounds like he'll play back at you with nothing. As hard as it is to play AK when you miss the flop in limit, it's even tougher in big bet, because you'll never have odds to draw if there's action. Good luck.