General question: Overpair on a drawy board

[Noir_Desir]

I had a theoretical discussion on another board and would like your to hear your opinion on a pretty basic noob question:

Full ring game: Hero raises AA from middle position. BB calls. 100BB stacks. We get a flop where straight and flush draws are very possible (say T93 2 hearts). We make a standard c-bet of say 6BB in an 8BB pot. Villain checkraises potsize (26BB). What do we do here?

Chen's "Mathematics of Poker" mentions it would be better not to committ all the money on the flop if he has a draw, but wait for a blank turn. So my gut feeling would be to call and committ with a big bet on a blank turn. Or is shoving the flop standard? Or would it be better to fold?

Assume no reads. What changes if we raise from EP / LP?