This is a spot where I now just bet turn and river expecting folds from a number of better hands.

I don't expect him to have Ax very often opening UTG and checking the flop back. So unless he spiked the king he's going to struggle to find a reason to call a river bet.

While I don't think calling pre is bad given the limit I'd fold this hand vs. confirmed tight UTG player.

As played it's either check down (which is ok since you kinda need to assume that villain doesn't have huge preflop range advantage in order to make this pre-flop call) or bet/bet bluff starting from the turn to fold out better pocket pairs.

+1 to starting to bet the turn when the flop is checked through with the intention of barreling on the river.

There are a ton of hands that villain can play this way that are ahead of us that will have to fold to this line, and the hands that we are ahead of that villain folds still have a decent bit of equity against us. As turlock mentioned unless villain has binked a king on the turn we will almost certainly win the pot if we take this line.

Turning your hand into a bluff seems pretty reasonable. By checking down you'll win against 22-44 if villain doesn't decide to bet them at any point. That's a really narrow range you beat and I think it's unlikely villain tries to check down something like Q-high. So while you can win a small amount of the time by checking I think you can win much more by going bet large bet large. Villain should rarely have an Ax, and even if he binked a Kx on the turn it's still tough to call down 2 big bets with 2nd pair.