Very wierd hand by him.
I would check behind as you did.

Im not sure why he checks the river I dont think he would check call with his hand.
If he is a good player I think he will fold OR check raise the river(Turn his hand into a bluff). I never think he is gonna call it since you called 2 streets and then bet river, it looks strong on this board. If you would bet and get check raised I think its prettyy damn hard to find a call.

Some player maybe prefer to bet and fold to a raise but Im not, not when you have this hand on this board.

I'd be raising the flop. Vs an unknown you have no real way of knowing how value heavy or bluff heavy he is and even if he's value heavy you beat lots of his value hands anyways. It's a spot where he should never have sets so unless he flopped a straight you're ahead.

If you don't raise flop you can raise the turn as well.

River you should still be able to get value. I think you can go for a small bet/fold. If he's scared of the flush then I don't think the best way to get value is by betting huge. I really doubt many players are donk bluffing a flush draw twice just to check it when they hit so I expect you to be ahead a lot. That being said I don't really expect you get bluff checkraised on the river either so even though I think it's unlikely he has a flush I would fold to the raise.

This would probably be near the bottom of my betting range though. I would check back all 1 pair hands.