Do I value bet this? Villain is 40/14/1.7

$0.25/$0.5 Pot Limit Holdem
4 players
Converted at

Stacks:
CO ($8.15)
BTN ($28.60)
SB ($79.40)
Hero ($50.85)

Pre-flop: ($0.75, 4 players) Hero is BB [Kc]
2 folds, SB calls $0.25, Hero raises to $1.5, SB calls $1

Flop: [3h][7d] ($3, 2 players)
SB checks, Hero bets $2.5, SB raises to $6.5, Hero calls $4

Turn: ($16, 2 players)
SB bets $11, Hero calls $11

River: ($38, 2 players)
SB checks, Hero ???

I'm all in favor of value betting rivers, but the action makes me think a check is better.

The best value betting is where someone is callling you down because they don't give you credit for even a very good hand. The call light.

This guy is raising the flop. He's leading the turn.

That's a different type of opponent.

I'd probably check behind here. If he has a missed draw he's likely folding anyway. So checking also gives you info because you can checked the mucked hands and gain some info there.

If he has a set we're dead, about the only other thing that makes even remote sense is that he flopped bottom 2 and just fot counterfitted.

However since he is passive and has shown aggression the whole way he may have just filled up and is looking to get fancy, which is a possibility as well. Maybe it's a little WT but I think I like a check here.