playing high PPs OOP facing overcards on flops

Having a high PP OOPS but facing a flop that has a high card is a situation that always makes me feel uncomfortable. For example, I had a hand where I had QQ on cutoff. Raised to 14c (3.5BB) and got called by BTN.

Flop comes Kh9c5d. Check check.

Turn is 3h. I check, he bets 22c into 34c pot. I called. I

River is a 5c. I check again and he checks. He had 8h9h and I win a tiny pot.

In the past, I would have played it a lot more aggressively, but lately I've become much more timid, leaving value on the board.

I know about the WAWB theory, where in the situation above a raise would theoretically fold out hands I beat and get called by those that crush me.

But at the same time, I am missing out on value on draws and if I just check/call to showdown, I am basically just letting villain see a free card and let him bet only when he hit his outs. For example, he is not going to river bet with a pair of 9s unless he makes 2 pairs on the river.

I only gain if he river bluffs, which at 4NL is rare for most players.

I really dunno what is the best course of action in these situations.

Playing OOP sucks.

I just generally cbet a flop like you described. If I didn't cbet the flop I'd bet the turn 100% of the time. I think trying to get 2 streets of value is really what you should be shooting for.

+1
I usually almost always c-bet flop with PP playing OOP. Firing a second barrel could be dangerous if he calls though, so slowing down a little on the turn and river is suggested.