SB had 9, J (two pair, Jacks and nines).
Hero had A, A (one pair, Aces).
Outcome: SB won $2.70
Did I play this wrong? Did not expect SB to have any of the two pair hands to be in his range after the re-raise preflop. Would've expected JJ + AJs+ as he had been playing very tight preflop before this hand in which case there was only one possible hand that beat me.
As a general rule I'd make the 3bet sizing 3 x the original raiser + an additional raise amount for any callers. So in this case I'd make it 24c to go.
As played i think the shove is the right move since SB is short-stacked although it's a pretty horrible spot. You're kinda hoping he's doing this with AJ, KJ or QJ and you're getting ~ 3/1 to match his all-in.
You could also call the raise and if button also comes along shove to any turn card.