You have AK or AQ in late position and someone has raised 3xBB. You reraise to 9xBB and they rereraise to 27xBB. Now what do you do.

To avoid replies saying "read dependent" could you give examples of how you would act given different reads or stats, and perhaps even the "in a bubble" action you would take given not enough hands played with your opponent for a solid read.

In a bubble I think KK/AA are very likely (although by no means the only possibilities) and I would not have a clue how to play if I called and hit the flop.

I say "very likely" because over the small 15k hand sample I have at 25NL it is my experience that even those players with laggy stats will often fold to a 3bet preflop without a huge hand and that 3 betting gets a lot of respect. It does get called sometimes by the opponents who perhaps have a "big pot" hand and are calling with implied odds in their favour, but when it is repopped, It's usually a monster.