KK in a big pot

[detruncate]

Check/call the turn. There are no legit pf 3-betting hands you're ahead of. 3-betting ranges are usually fairly reasonable in general and this guy seems even more likely to have a tight 3-betting range (based on his stats so far) despite your MP open raise.

We don't want to pay 2 bets to see the river with our OESD unless it's going to increase our equity. Giving a free card to a diamond is the lesser evil -- Villain doesn't have a single diamond when he's behind unless he 3-bets AQo (possible given your MP open raise) or AJo or worse (seemingly unlikely) or a PP < T (also seemingly unlikely).

What about a c/r? The other guy might have a diamond, but he's not folding a flush or big flush draw on a non-paired board even facing 2-cold. I can't see how we make up enough in increased equity to justify spending 2 (or 3) bets since Villain also also has to be diamond free. We could probably fold to a 3-bet since Villain is going to be uncomfortable 3-betting with less than a flush, but I still don't think a c/r is even close to better than a c/c unless the pot is way bigger.