Villain has been pretty solid as far as I've seen, and his shove was instant

Hand #1336012294000858: Chelsea (6-Max) 12294
Seat 1: jodiii (41.80 in chips)
Seat 2: fox3699 (114.02 in chips)
Seat 4: stickdude (139.25 in chips)
Seat 5: bighugenoob (111.15 in chips)
Seat 6: AKM-47 (112.85 in chips)
Seat 10: ( o__ o ) (72.50 in chips)
fox3699: posts small blind $0.50
stickdude: posts big blind $1
Dealt to stickdude [ ]
bighugenoob: raises to $3.50
AKM-47: folds
( o__ o ): calls
jodiii: folds
fox3699: raises to $10
stickdude: raises to $35
bighugenoob: folds
( o__ o ): folds
fox3699: is all in
stickdude: ????

It's about $79 more to call.

During the moment, I always felt with KK preflop at 6max.

But let's do some math:

The pot is laying you 1.9:1.

So that means that even if he has AA 2/3 of the time there, you are a coin flip EV wise (since you are way ahead of the rest of the range of AA/AK/KK/QQ and some smaller group of overplayed less strong hands).

I think you'd have to feel that he has AA there 75% of the time or greater to even consider folding. That's pretty rare to have a read that solid.

Call and it's not close.

You've put in too much pf to fold.