Hey mate,
When making your cbet, try to think about:
1. which hands you want to fold
2. which hands you want to call
3. which turn cards you don't want to see.
4. what do we do if he check/raises us
5. pot size for later streets
Do numbers 1 and 2 match up with the hands that will ACTUALLY call, and those that will ACTUALLY fold? Are there a lot of bad turn cards for our hand, or do we not need to worry that much about protection? Generally 3 ties in with 2 in the sense that you want draws to call you but you don't want them to hit their draws 
So what to do on this flop? What hands do you see calling here? Maybe some smaller pairs, but I think 22 - 55 will fold their bottom pair here. So you're maybe getting called by 88 - JJ which you beat. You're getting called by Kx always and 66 or 77 sets obviously. You might occasionally get called by an Ax hand, which would be weird but i've seen it happen. An overwhelming part of his calling range is going to be Kx hands which will never fold this flop. Which is bad, because we have very little equity against those, and heaps of equity against the smaller pairs who will sometimes fold.
What do you do if he check raises? You have a very good hand. Not the nuts, but 2nd pair definitely has showdown value. You are quite vulnerable to being check/raisebluffed off the best hand by some spewy fish, unless you're happy getting your whole stack in here with 2nd pair which would definitely be overvaluing your hand.
Pot size for later streets? Well, we aren't necessarily trying to get all our chips in the middle when any Kx crushes us. Therefore we don't need to build the pot. In fact keeping it small is good, because it makes it cheaper for us on later streets to call him down to a cheap showdown.
So my conclusion: check back on the flop.
Here's why I check back: Checking back allows him to bluff the turn with a lot of hands that would otherwise have folded to your cbet. Equally, he will bet Kx hands too, but his range is a little more favorable to you on the turn. It keeps the pot in control, so we aren't horribly committed if he shoves the river.
(also, as played: definitely call river with those pot odds)
Not sure why I just wrote an essay for a hand response. Guess I just felt like articulating some (albeit fairly basic) post-flop logic instead of just saying "i do this instead".