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I think if you get AA heads up, you want to act like it's just another hand. So, if you have been limp/checking, limp (SB) or check (BB). If you have been throwing down standard 2xBB raises, then throw it down again (UNLESS he's camping, and will fold to a raise most of the time).
I think, in your case, the limp was OK, but you have to bet the flop, since you are a short stack. If he's holding 2 spades, or some garbarge like 46 you can't let have a free turn. If the situation was reversed - you are the big stack - then you can check the flop and hope he bets into you, because should he get lucky and draw out, you still have him covered.
Note that you could have gotten completly hosed here - 3 might have completed a straight, and now you have to go all in against a big stack.
I think with the short stack, limp PF, push the flop with a JXX is the proper move. Push pre-flop is reasonable, but only if you are sure he will call you.
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