[BDaws]

I normally would bet the flop, but I don't think checking is that bad. He might fire with an underpair which is great because you certainly aren't getting value from them if you bet and they have very little chances of improving.

However, there are definitely more hands than AK that you can get value from. With position, wouldn't he peel light with KQ, JT, KJ, AT? That's if he calls with them preflop which I don't know.

I would bet a little more on the turn. 18-20 works.

On the river, I think I like a b/f for 35 as SN suggested. You play is consistent with a Kx type hand so I don't think he will ever bluff raise unless he doesn't read hands well and just bluffs wildy.

So the times he has Kx, you lose 35.
The times he doesn't you win the pot, but never get called by a worse hand.

I think this is better than c/c because he will likely bet more than 35 if he has a K (so you are losing more when he has a K than if you would've just b/f $35), and will certainly put you to some tough decisions because we don't know his bluffing frequencies that well.