A KK hand, I might be rusty (6 max)

[nrinker]

With the villains hand range, you either need to get it in on the flop or fold when he raised you.

Calling and pushing the turn is horrid. If you call then push the turn, the villain still calls with the better hands you mentioned, but also gets to draw/bluff your ass out if a scare card hits for you.

Calling, then pushing the turn accomplishes nothing.

If the villain has 99-QQ, you may fold them you may not. Im leaning towards not though, if an over card comes on the turn and you push because it is "safe", then you could possibly push villain off the hand he was going to call with on the flop.

This is why you absolutely need to fold or 3bet(large or all in) this flop.