I played this hand about a week ago from when I'm posting this so not exactly sure of my thought process on the river. I think we can go for the bet/fold option with the relatively safe assumption that he will only shove with hands that beat us, going around the same size that villain does on the river.

When I check and villain bets, I think that I was thinking at the time that villain is going to check behind pretty much all worse hands, even a hand like AK probably will check behind as it's hard to see a hand worse than AK that plays this way and calls the river.

Now looking back on it I see it a little differently. When I check the river I think (and I think that villain thinks) that I never have a flush here. Is this enough ti make villain bet hands like A7/AK/K7 for value on the river? I'm not sure, mainly because if I don't have a flush here, what am I check raising the flop with? It's gonna be sets, possibly K7 and hands like gutshot + backdoor flush draw.

Is this river fold too tight? Would a bet/fold line be better? Do you think villain (or you in villain's spot) bets a two pair hand on the river?

Thanks!