How often will you fold an overpair to a 3-flush board?

[WarDekar]

There is a specific hand that brought this to question, but it's mainly just a general question so I won't post that HH. Say you have QQ-AA in level 3 and put your normal raise after there are several limpers, and all but 1 fold so you're HU on the flop. This stack can cover you.

The flop comes low but all one suit, no straights possible. You put in a feeler bet, and he pushes. I realize this is a bit vague as you don't know how much you have in the pot, etc., but how much do you give the guy credit for a flush, or does he just have TPTK, a set? What if you have one to the flush also so you could possibly pick up a higher flush? What if you had flopped a set?