[Genz]

I don't like playing KK for set value. And a K on the board will often be the highest card so you can't extract from an overplayed TP as you can with a smaller set. So you need a lot of luck to either get a flop of AKx or someone holding the case K. So I think trying to get it all-in preflop is generally the best idea with AA and KK on these limits.

And btw: I've been running card dead on tables over samples like this before and had nittier stats than villain. Don't forget that he could just be running very cold and doesn't necessarily have AA, KK here.