preflop - his min re-raise shows AA, and that he wants to keep you in the pot and go heads up with his AA.

flop - i probably would have bet around 3/4 of the potsize here (hoping that he will raise me here) so that I can build the pot with him on the flop. He min raises you back on the flop right after u bet into him - showing you that he has an overpair to the board: either AA or possibly KK. At this point I would re-raise, knowing that he will probably stay in the pot with me. Most likely i will re-raise to about 2.5 - 3x his min raise. If he calls, then I push all in on the turn.