[LearnedfromTV]

Checking the flop is fine. It encourages action from hands you have beat, none of which have many outs against you. A jack, QQ,TT-88. I would bet the turn, especially with the club hitting, but either way - checking the flop is enough weakness, you're definitely getting called by a pair. Having checked the turn, bet 2K on the river to get value from hands that will check behind, having to call a raise but hating it. The same medium strength hands that are willing to bet the turn will usually check behind on the river.

Betting the turn makes it easier to fold to a push, although I'm not sure I would, depending on the opponent. Point being, value betting the river is now really awkward since you have no choice but to pay off a king. Ideally, you'd like to structure the betting to avoid going broke when he has a K. Tough to do this shallow though, so focus on getting value from weaker hands.

Edited to add: With 6K in the pot and 5K behind on the river, I think pushing the river is best *if* he has you covered by enough that he can comfortably call off 5K on the pot odds with a hand like AJ or QQ or even TT-99. Especially if he's the type to call (although you said no read). If 5K would break him, you need to bet less because there are hands he won't be willing to go broke with, even for a 16K pot. Since you're going broke when has a K, you need to get as much as possible when he doesn't. The full 5K if you can, or, more likely 2K-3K. 2K-3K will sort of function as a blocking bet also, because it will be hard for him to raise without a K, and you take away his ability to push you off the best hand because you're obviously committed to calling. Of course, you still have to call the raise because AJ or QQ can make a value raise just often enough that you're stuck.