Preflop
Like the 3-bet
Flop
Like the C-bet
Turn
I think, you have to bet again. You have K high, you picket up a gutshot to go with your other equity, and there are certainly some hands, that will call one bet but fold to the second.
River
As played you have to call. When you check the turn, you induce bluffs from him on the river, so obviously you need to be ready to snap them off with your bluff catchers. Some times people will also misread the situation and think, your hand is weaker, than it actually is, and bet a hand like second pair thinking, its for value.
__________________
|