I think you should value bet the river generally, its hard for him to have 2pair unless he rivered it, or he could definitely have rivered a flush but checking puts you in a guessing game you just dont want to be in and betting will definitely get you some value. $5 - $5.5 on the riv looks good, folding to any raise. now that you've checking I think its an easy fold with his bet sizing.
I also think you should consider strongly checking raising the flop |