SDK, you say that the villain won’t check the river with anything stronger than the hero, but answer me this: What hands are we representing on the river?
In regards to the villains range:
That turn raise looks nutsy as fuck. You think he has lots of draws but I’m not so sure...
The J of hearts being on the board takes a lot of the heart draws from his range. You’d expect him to raise the flop often if he had hearts too. And so that leaves nearly no heart flushes in his range.
The turn card brought some more straight draws but would TQ really call the flop bet? Perhaps. Would he then raise the turn with QT after we barrel? Unlikely. It’s very unlikely that this dude will make two dubious plays with a straight draw. And so we can take most of them out too.
He could have floated the flop with two diamonds but again, with the Ace and 9 on the board he can’t have many of these hands in his range. It’s quite possible that QT of diamonds floated the flop, but it still doesn’t make much sense to raise this hand on the turn.
His raise on the turn is pretty small too, this, again, takes many of the draws from his range. I’m almost certain this guy doesn’t have a draw.
Now onto the value hands in his range:
If this guy had a AQ or AK you’d expect a raise preflop. If he had AT or below you wouldn't OFTEN expect him to raise on the turn. That basically leaves no likely single pair hands. The only real possibility I see is the AT that wants to take a little extra value off draws. This is a bit of a crazy play but it is BB vs Button on an A high board which makes crazy plays somewhat justified.
AJ and 44 often raise the flop. 99 usually folds on the flop.
There is only one hand in this guys range that makes perfect sense to raise on that turn: A9o. Draws don’t really make any sense but 44 still does. And so I think our best strategy is to fold to the turn raise.