KK fold to river push?

PokerStars No-Limit Hold'em, $0.25 BB (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

CO ($18.10)
Button ($13.30)
SB ($8.50)
BB ($44.85)
UTG ($8.15)
UTG+1 ($12.50)
Hero ($27.10)
MP2 ($1.20)
MP3 ($12.55)

Preflop: Hero is MP1 with K, K.
2 folds, Hero raises to $1, 3 folds, Button calls $1, 2 folds.

Flop: ($2.35) 3, 6, 3 (2 players)
Hero bets $1.5, Button calls $1.50.

Turn: ($5.35) A (2 players)
Hero bets $3, Button calls $3.

River: ($11.35) T (2 players)
Hero checks, Button bets $7.8 (All-In), Hero folds.

Final Pot: $19.15

Fold...

Check fold turn is fine too.