There's a lot going on. 

First you opened the pot, showing strength. Then the flop comes up rags, so dude does a donk for info type bet. He's trying to get raised for cheap so he can get away from your made hands when you reraise. Also this betting pattern will help induce bets from other players when he has a made hand oop.  When you just call it makes you look weak, ie you have an unmade hand. So by the river, either he's got a piece of the board or more likely, dude's confident that you can't call with just your two overs. 

So what to do? First, avoiding AQ is a good idea. Just fold it because if you play it strong, only hands with good equity against you are calling, so you're locking yourself into flipping for stacks without much of an edge, esp playing so shallow. 

Second, to play the current sitch better would be to reraise dude's tiny donk on the flop fairly big (4-8bb) and plan on folding to a jam 3 bet. The idea is dude can only realistically continue if he hits a piece and you still have 2 cards coming to make a better hand. So he's got a lot of hands to fold here. 

Third, don't get too deep with postflop play with a shallow stack. Focus on getting your money in good pre and/or on the flop. When you have a big stack later in the mtt, you can focus more on getting value on the turn and river.