KK reraised pf

Reads: Villain seems to be mostly a nutcamper, He rarely raises pf, and when he does he bets strong, close to pot. He does play a decent amount of hands, but mostly limp calling or calling raiess. Ive never seen him reraise pf.

Party Poker
No Limit Holdem Ring game
Blinds: $0.50/$1
10 players
Converter

Stack sizes:
UTG: $18.50
UTG+1: $105.80
UTG+2: $110.45
MP1: $131.95
MP2: $221
MP3: $103.05
Hero: $173.60
Button: $60.25
SB: $333.32
BB: $101.50

Pre-flop: (10 players) Hero is CO with K:club: K:spade:
3 folds, MP1 calls, 2 folds, Hero raises to $4, Button folds, SB raises to $12.13, 2 folds, Hero calls.

Flop: J:heart: T:diamond: J:spade: ($26.26, 2 players)
SB bets $23.05, Hero calls.

Turn: 2:club: ($72.36, 2 players)
SB is all-in $297.64, Hero folds.
Uncalled bets: $297.64 returned to SB.

Does QQ push after i smooth call, i think this is prob AA or KK, and i should prob not be calling Ais hoping for a split??

Results:
Final pot: $72.36

IMO, good fold.

I think that if you don't plan on pushing a flop that is not too scary then you need to 3-bet preflop.