Have you ever used an equity calculator before? You should practice putting your opponent on a range and calculating how much equity you have against that range and how much you need to call. It's not a matter of “Am I ahead or behind”, of course he will play some hands better than KK like this but that doesn't mean you should fold because he will also play plenty of worse hands like this. You have to learn to estimate how you are doing against all of the hands he could play this way, and that requires doing some homework away from the tables. FWIW this is a very clear call.

I understand that, you're saying that there are hands that you have to fold when you are deeper but that you can get all in with when you are shallower. That's true, and essentially what's happening there is that you are getting leveraged out of the pot. Although you'd have a +EV call if you could get all in, your hand will play poorly against future betting and consequently you have to fold. You're getting forced off of your equity, it's not a good thing and it definitely does not make you less likely to experience losses because you are deep-stacked.

I'm not sure there's a necessary relationship between variance and stack depth, but most likely deeper stacks = more variance because there are more decisions to make, and every one of those decisions has variance attached to it, and the biggest decisions/pots are of course bigger than they are when you have less money on the table.