KK against a fish

Villain is a fish (64/5). Flop and turn pretty std, just trying to get value. On the river I decide to check and he shoves. Std fold or should we call?

Edit: I think what made the river awkward was my bet-sizing. Bet bigger so he has under pot left on the river?

PokerStars - $0.02 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

MP: 290.5 BB (VPIP: 19.57, PFR: 10.87, 3Bet Preflop: 5.88, Hands: 46)
CO: 85 BB (VPIP: 64.10, PFR: 5.13, 3Bet Preflop: 0.00, Hands: 39)
BTN: 100 BB (VPIP: 18.29, PFR: 13.41, 3Bet Preflop: 4.00, Hands: 82)
SB: 79 BB (VPIP: 55.56, PFR: 33.33, 3Bet Preflop: 25.00, Hands: 9)
BB: 65 BB (VPIP: 17.95, PFR: 10.26, 3Bet Preflop: 0.00, Hands: 40)
Hero (UTG): 208.5 BB

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has K♣ K♥

Hero raises to 3 BB, fold, CO calls 3 BB, fold, SB calls 2.5 BB, fold

Flop: (10 BB, 3 players) 3♠ 7♦ 9♣
SB checks, Hero bets 6 BB, CO calls 6 BB, fold

Turn: (22 BB, 2 players) 2♥
Hero bets 14 BB, CO calls 14 BB

River: (50 BB, 2 players) A♣
Hero checks, CO bets 62 BB and is all-in, fold