It is interesting looking at game theory from an aggro players point of view...
If he is holding a hand like A8 suited and just shoves all-in preflop for a lot more, you've gotta assume that the opponent is going to fold a decent amount of time (as I believe you should have folded the 66). And then even if you get called all-in with your A8 suited, you are still only a 67%-33% against a big pair (vs KK, you can hit an ace for the win) or a big ace (vs AK, looking for an 8 for the win).
[Granted, when you have A8 and are up against AA, you are crushed].
Some aggro-people could rationalize making this play with A8, assuming that your opponent will fold to a big all-in bet a decent amount of time, and you are still in decent shape to suck-out when they call.
With that being said, I probably would've just called the small 3-bet and hoped to hit a set.
...But then even after you 4-bet and he goes all-in, I think calling was a bad play here as well. When he decides to go all in, what is he doing this with? Even if he has a hand like A8, it is still a coin flip. I feel like most of the time in this scenario, a villain will have an overpair and you will be crushed.