Getting levelled in 3 bet pots

[BGnight]

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I'd check behind here w/ AA,KK vs this villian as long as I had a diamond. I love letting these overaggro monkeys hang themselves.

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If someone is calling 3bets insanely light and check/raising every flop why would you do this?

edit: I'm seriously confused by this entire thread

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sry, I don't buy he c/raises light. I'm just taking into account he's aggressive in 3bet pots. Just because someone is capable of bluff pushing 3bet pots doesn't mean they're doing it in high frequency. If you can find a flop safe enough to check an overpair your almost always going to get bluffed on turn when villian has air.

As for having AK, what about checking flop and pushing most turns if he bets?