Push or Fold
I think calling is about the worst thing you can do here. There's already about $90 in the pot (PF $50 plus the $38 flop bet by MP), so if you call it's about $130 in the pot, and you both have $150 or so left. You're basically gonna be committed to playing your stack if you're going to call down here, because he's probably gonna bet the turn and/or river.
You've either gotta trust that you do have the best hand (and push now, in case he's on a drawing hand that may fold), or figure you're beat (pocket TT or 55 might both play the way MP did) and fold. It's a tough decision.
What range of hands is MP likely to have played this way? If I read the stats right, he's a reasonably tight player, so I would put his range at TT, JJ, AK and AQ, with 55 an outside possibility. Without more info I can't really guess which of these he may have.
Personally, I find his bet suspicious - he bet less than the pot-size, which usually means he wants to get a caller. I'm inclined to fold here, but if you had any reads about his tendency to bluff or stop-and-go, I wouldn't say pushing is bad.
Side note: why do people always re-raise with AQ or AK on the button when a raise has already come in? If someone already raised, I think of these hands as drawing hands, and am willing to flat call to see the flop. Any early or middle position raiser is likely to call any re-raise I make anyway, so why not keep my money for the flop, so I can fold (and save the money), or bet harder (in comparison to the smaller pot size)