AQo utg flopped middle pair in multiway pot

I don't see many worse queens calling an open from UTG, plus he is a bit loose he might call KQo.
When he check behind on the turn he tries to rep a K, or he might slowplay a boat to induce you to bet the river.
I think that's a fold.

Villain is shortstack so we can call and make a note.

How about cbet OTF? Villain shouldn't have many Qx hands but he shouldn't have many Kx hands either. This is multiway and the board is quite drawy so I wouldn't want to give free cards. We might get value from pockets and draws by betting OTF.

I agree with cbetting the flop. Mainly vs the overcaller in the blinds. We often have the best hand otf and don't want to get outdrawn.

As played you just HAVE TO bet the turn for value, there's no way around.

OTR it really looks like 33's to me which got there because Hero meant to slowplay a hand should bet for value and protection.

Which range would you give Villain?
What are your pot-odds on the river?

Without considering these things I would not make any wishy washy assumptions if we should call or fold...

The reason for cbetting flop is not that villain doesn't have Qx or Kx. The reason is that there are still plenty of draws that we can charge.