It's far too sweeping a generalization to say aggros will always outplay tight players. It completely leaves out not so minor factors like skill differential and position.
As for the example, when you play AK vs T9s, especially in position, you won't win every hand, but unless you have major leaks in your game, you will make a nice profit over a meaningful sample size.
And while it's hard to fault re-raising the flop, it's certainly not the only possible choice. If you're ahead with your TPTK, which you are against a large majority of his wide range, particularly if he's firing all his air, which is likely since he is aggro after all, you want to try to get him to put more money in the pot rather than to fold him out.