Set of jacks loses to Flush on river

Once the original raiser folds to my 3 bet and i get called by the person who flatted the first raise i feel it’s likely he may have a small to mid pair or a semi connecting hand.

It’s quite a draw heavy flop so i expect a lot of bluff raises here as my opponent will hope i fold most Ace X hands.

I lead the flop for just under the pot which pretty much commits my opponent to this hand. If he wants to draw to the flush Im happy with him to call. I will never check back twice here and let my opponent get to the river for free. I do expect the player to fold most of the times without making a pair or the flush since im never folding here.

There’s so much in the pot by now its hard to fold for £700 to win £5200.

I expect the player to jam most turns with the A hearts even though i will rarely fold my hand given the stack sizes after betting the turn.

There is still the chance this player has a small pair and feels he is ahead of Ax when I bet the turn. Most of the time the player will call the river with any made flush here but I don’t think check folding this river in this scenario is right. There’s a good argument to say the player has a flush most of the time by the river and therefore in the long run this would not be a profitable bet.