c-bet the small stack HU on draw heavy board?

[CCCP]

A situation I think we see often, how do you play this one?


Villian is a loose small stack (25BB or so) and limps in (any position).

You are in the SB with AQo, and raise it up to 5x, and Villian calls.

Flop is draw heavy. maybe 4c5c9h
Villian is loose, so could have just about anything here: two overcards, SC,offsuited connectors, Axs, Kxs, Qxs.

If you c-bet 1/2 pot, you know villian will probably stick around, even with QJ/Q8 type hands. If I check, I expect villian may push.

Do I c/f? Push to force him to a decision now? Make the c-bet anyway and hope he lets it go?