How do you play against a player who is raising every hand preflop and betting every hand on the flop and has you outchipped almost 2 to 1 ?

I actually had more chips than him at one point. I had $6000 and he had $4000 but then I just kept getting horrible hands and had to fold preflop many times because I just didn't get hands good enough to call with so he eventually knocked the 3rd place player out and then we were heads up and he had a 2 to 1 chip lead. I trapped him a few times but then he just kept folding to me.

I'm rusty at tourneys since I haven't played them in a while. So I limped in with A4 since he likes to raise a lot but this time he just calls. I flopped a pair of aces and checked flop and checked turn and he finally bet on the river and I reraised him all-in and he called and showed QT but I have no idea how a QT beat me. It was at pokerroom at the window disappeared before I could figure out what he had. For all I know, I had the best hand. Was it correct to slowplay my pair of aces ? I mean a pair is good most of the time heads up. The guy was betting every flop and then he stopped because I kept trapping him.

Can't really tell you if slow playing here was the correct play with out knowing the board.

With QT he probably beat you with a straight if K,J came out, or a flush if 4 suited came out.

I think you'd know if QQ, TT, or QT was on the board.

Normally I try to slow play only monster hands against over-aggressive players. Flop trips/straight/flush even top two pair if the board is right. I'll usually push back with small edges like TPTK or a weak A like you had. The reason is if he's playing alot of different hands, I don't want to give him too many free cards to suck out on me. I'd rather take the small pot with my AA 4kicker on the flop, or make him really pay to catch his runner runner straight/flush. You're gonna need as many chips as possible while waiting to get the right cards to trap him. Winning small pots is essential to staying alive.

By slow playing medicore hands, you're letting him beat you by either sucking out on you, or betting you out when scare cards come down.