I play them aggressively. Shoving early with AA and KK is much safer than allowing your opponent to cheaply improve their hand and get good
odds, but generally you don't want to shove right away (first you raise and re-raise). AA and KK are not invincible. They have very good odds pre-flop (~85%
equity), but in the end they're just high pairs.
I also play QQ and JJ aggressively, but they're somewhat weaker, especially JJ. So I 3-bet with JJ, but I would generally fold JJ to a 4-bet against a tight player.
Note that JJ has 78% equity against any
random hand, but people rarely play
all hands. Especially against a tight player, with a range of say 10%, you only have a slight edge pre-flop (59%). And if the flop comes with A x x, then you only have 37% equity, since the probability of a tight player having A is much higher than a loose player (otherwise they would have folded to your raise).