KK between fish and solid regular on paired board

[I KILL]

Grabbed byHoldem Manager
NL Holdem $4(BB) Entraction
SB ($719)
BB ($455)
Hero ($680)
UTG+1 ($905)
CO ($422)
BTN ($703)

Dealt to Hero K:diamond:K:club:

Hero raises to $14, UTG+1 calls $14, fold, fold, SB calls $12, BB calls $10,

FLOP ($56) 3:diamond:7:spade:3:club:

check, BB bets $56, Hero calls $56, UTG+1 raises to $120, SB folds, BB calls $64, Hero calls $64,

TURN ($416) 3:diamond:7:spade:3:club:5:diamond:

check, check, check,

RIVER ($416) 3:diamond:7:spade:3:club:5:diamond:9

BB bets $321,

BB= fish