[LateFlag]

I think you played it fine.

There's not much reason to bet the turn. If villain has the flush, he's check-raising you so you'll end up charging yourself two bets to try to redraw against him. Granted, a bet might fold out AK which obviously isn't a bad thing, but checking behind might allow us to extract a bet from that hand on the river.

Given that you checked the turn and villain checked to you on the river, I like the river bet. Villain pretty much has to call this since you've both shown weakness, so this is a fine value bet.