NL50 KK, rivered set

Microgaming - €0.50 NL (6 max) - Holdem - 5 players
Hand converted by PokerTracker 4

Hero (BTN): €55.28
SB: €50.66 (VPIP: 33.33, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 6)
BB: €57.36 (VPIP: 21.62, PFR: 21.62, 3Bet Preflop: 7.69, Hands: 38)
89% agg.freq.
UTG: €76.83 (VPIP: 32.05, PFR: 6.41, 3Bet Preflop: 3.45, Hands: 81)
CO: €50.75 (VPIP: 27.27, PFR: 23.64, 3Bet Preflop: 18.75, Hands: 57)

SB posts SB €0.25, BB posts BB €0.50

Pre Flop: (pot: €0.75) Hero has K♠ K♥

UTG calls €0.50, fold, Hero raises to €2.00, fold, BB calls €1.50, UTG calls €1.50

Flop: (€6.25, 3 players) T♦ A♥ 8♣
BB checks, UTG checks, Hero checks

Turn: (€6.25, 3 players) 3♦
BB bets €4.00, fold, Hero calls €4.00

River: (€14.25, 2 players) K♦
BB bets €10.00, Hero raises to €23.00, fold

I decided to call the turn, because he could have some draws/bluffs.

On the river? The flush got there and he can have that. He can have QJs. But he could also have AT/KT/88/TT/33, so i decided to make a small raise and fold to a shove?