It's not the min raise alone... it's the limp/raise from early, the min reraise, the controlled raising war, rather than lunatic raising war, and, naturally, individual player tendancies. This guy who calls your shove with JJ... was he running at 4% pfr? JJ is easy fold here so you have yourself a fish who calls too light. Did you have notes or stats to help you decide this? Fwiw, when you shove I'm fairly sure you don't have AA, unless I got notes on you to determine otherwise, or unless you know this guy calls shoves light. If it were against me, it looks like QQ, KK or maybe AKs (hence JJ being easy fold), but not AA. He might have AA, but it's not AA only. It's AA only when someone l/r from UTG and then min raises an aggressive raiser twice before we even see a flop, such as in your first hand, or it's AA only, for me, when a serial limper suddenly finds the raise button against a 3better, even though he didn't know where it was when he had AK not so long ago.

"You're seeing monsters under the bed."

Maybe. Like I say, I raise this pf to high hell the vast majority of the time, I can take it when it runs into AA or when they suck out, it's not big pot fear or anything because I need only open up tracker and see KK is a hugely profitable hand. But, it's not the nuts... even as I reassess this hand and hear you all say "SHIP IT!!!" I'm still happy I got away from this cheaply.