Unless he is a complete nit i'd shove here. But i'm not a fan of playing HU in cash games, so it is a bit of a hard choice because of how deep stacked you are.
But if this was a SnG, i would shove without a moments hesitation. If you are in HU play, and you find yourself 2 pair vs top 2 pair or 2 pair vs a set, then you should get stacked because such situations are very rare in HU.
If he isn't tight, he could have Ax and make the same choice. I would shove...if he has AJ/JJ/99 then bad luck, but i would imagine his reraising range is substantially wider than that.
You limped, he raised, he isn't going to be happy with you reraising his cbet if he hit the flop after you limped and the flop came all high cards, so i think that in the vast majority of cases you are way ahead here. You only min raised, which is often taken as a sign of weakness, so i really do not think he puts you on much of a hand. I'd probably shove vs a nit here as well.