[skp]

Your post implies that checkfold is out of the question. If so, then betting out certainly seems like a better play than checkcalling. This is because he will call with ace high often (as the river doesn't add any threats to his hand). He will also value bet overpairs if you check as he might now assume that you are checking because your 97 has been counterfeited (or perhaps 'overcoated' is the more appropriate term). So, you don't save a bet by chceking when he has an overpair.

It's hard to see what draw he could have with which he would bluff if you check. There are a few such draws but they number far less than calling Ace high hands or overpairs.

So overall, I like the bet.