Bet the river?

[Aceium]

Yes you should be betting this river. You don't think that he floated you on the flop with 78 do you? IF you do you can check behind. But I don't think he's playing this way with 78. If he had decided to float with it on the flop I might think that he would choose to semi-bluff with it on the turn.

But on the river here, there should be many worse hands that will call you. Only straights are beating you here so I would try to extract value from a lower set or two pair.