Oh sorry I thought you said you caught the set of 2s on the flop and got allin.

Yea as played its tough because he has such a big reraising range. You dont know if this is a hand he will lay down or not. I think your push after his reraise is very dangerous. I also think his call is pretty bad too but thats just me. The problem with raising 22 is that if you are just called you are going to hate any flop that doesnt have a 2. I think Id rather just limp => set.
Rather perversly an open limp on the button actually looks pretty strong here. It screams "Ive been waiting all night for this AA, please God dont fold".
If he raises you can call and sethunt, or just fold depending on how big the raise is.
This way you get to use your position to potentially steal it when he doesnt like it later aswell.

I think you both massivly overplayed your hands here.

If I have AA on the button here i bump up the raise amount slightly higher than usual because I think the big blind is likely to overplay and reraise a wide range of hands here.