I don't think the cbet is good in a vacuum. If you check behind and he checks again on the turn you can bet there with more FE and a flush draw.

If we could say it's a thinking player than you could argue for a bluff on the river, but I'd just give this one up.

About the cbet, if he decides to get cute and c/r there then you lose your chance at a K or T coming. The turn can be really good for you, so check and give it a 100% chance to come out. TBH, I think so many turns are scare cards that you could almost bet it blind if he checks a second street.