stars 5/10, river action?

[durrrr]

i bet 680 on the river, and villain thought about 56secs (60sec time bank) before folding what he claimed was JJ (i am very inclined to believe him). Ahnuld, on the turn if i raise, villain may push 2p, 77. That being said, if he pushes i must fold, as i am way behind vs. his pushing range (he doesnt often push 2p/77). Also, he is folding his overpairs a fair amount of the time- so i think this line wins less, and loses much more (although it does help me win the pot a slightly higher % of the time, but not much as villain rarely has even 6 outs, and at most he has 10).

I really don't know what i would've done if he check raised- and I still don't know what the best river bet was.