[Closed] NL2 set on a draw heavy board

Grabbed by Holdem Manager
NL Holdem $0.02(BB) Replayer
SB ($1.67)
Hero ($2.13)
UTG ($2)
UTG+1 ($1.21)
CO ($1.81)
BTN ($2.65)

Dealt to Hero 3♥ 3♦

fold, fold, CO raises to $0.06, fold, SB calls $0.05, Hero calls $0.04

FLOP ($0.18) K♥ 3♣ 5♥

SB bets $0.30, Hero raises to $0.74, CO folds, SB calls $0.44

TURN ($1.66) K♥ 3♣ 5♥ 9♥

SB checks, Hero checks

RIVER ($1.66) K♥ 3♣ 5♥ 9♥ 6♣

SB bets $0.87 (AI), Hero calls ??

Villain was 13/4 over 24 hands. I didn't really want to shove the turn, as I thought, that it would violate the main betting rule (not enough weaker hands would call, maybe A♥X, or maybe two pair, if he really is tight, and I don't see him folding sets/flushes), risking that he might actually backdoor flush with 1 :heart:.