As many others have said, with a 20BB stack you should decrease the size of your open raise to lose less, when you fold to a 3-bet. And you should do that even, when you intent to call off, because otherwise you are turning your range face up against any thinking opponent. Most good tournament players will mini-raise or go to 2,2BB, when the effective stack is 20BB.
And yes AJs is a call against a resteal from SB. You are supposed to be stealing wide, and SB is supposed to be restealing wide. Sure he will have JJ+ and AK/AQ in his range, but he will also have many other AX hands, that you dominate, and he will have KQ/KJ and some suited connectors. He will also have 22-TT, which you are "flipping" against, and even after mini-raising there are some dead chips in the pot, which you need to fight for.
Basically a situation like this is, what a program like ICMizer is designed for. It can tell you exactly, what hands you are supposed to call or fold given the stack sizes off all players, the payout structure etc. I have not made the investment yet, so I can not give you the exact answer, but I am pretty sure, AJs is well within the calling range. You are not thrilled, that he jammed on you, but the least bad choise is to call him off.
So basically this hand was just a standard cooler spot, which happen over and over in tournament. And in the long run they are just a wash, because just as often they will be the one with AJs, and you will be the one with AQ, and they will also get it in bad against you.