I really wanted the small stack to fold, and the BB to call... When the SS pushed, I'm not sure if I shouldn't have made it heads up w/ the BB by calling... I know a 3-way pot w/ AA sucks, but if the ss is allin, would you guys just play a sidepot heads up...?

PokerStars No-Limit Hold'em, $1.00 BB (8 handed)

SB ($39)
BB ($99)
UTG ($11.10)
UTG+1 ($67.45)
Hero ($105.50)
MP2 ($69.40)
CO ($60)
Button ($164)

Preflop: Hero is MP1 with , . CO posts a blind of $1.
UTG calls $1, 1 fold, Hero raises to $6, 4 folds, BB calls $5, UTG raises to $11.1, Hero raises to $105.5, BB folds.

Flop: ($124.10) , , (2 players)

Turn: ($124.10) (2 players)

River: ($124.10) (2 players)

Final Pot: $124.10

Results in white below:
UTG has 4h As (one pair, sevens).
Hero has Ad Ah (two pair, aces and sevens).
Outcome: Hero wins $124.10.

The real benefit of only calling this short stack all-in, is the fact that you might induce the other stack to reraise..

Yeah, that's what I was thinking afterwards... I was so ingrained into the whole "you want AA heads up" thinking, that my brain temporarily shut down when he pushed... It's still basically heads up me and BB less the $11 from the allin... I think I should've called and pushed hard on the flop and turn like I do when I'm normally heads up w/ Aces...