Flop two pair facing JAM

Wanted to post this hand & get opinions/ insights.

Pre flop : Seems standard. We open Q9s in CO. BTN & BB call. One thing I have noticed is a lot of players playing a flatting range OTB. Is that a thing? In theory, if youre gonna play a flatting range it makes sense to play flats OTB w hands like 55-99, suited connectors, & some of the suited Ax hands that we arent 3b (A2s, A3s, A6s, A7s-A9s).

Flop : We bet $.28 into $.80. I like using a small size here multiway (even tho I could see the logic in sizing up given board texture & a lot of bad turn cards for our specific hand). BTN folds, BB raises to $1.15. Given our specific hand - we block a ton of value hands that villain can have here. He nvr has QQ as that hand doesnt flat pre. There is one combo of 99 left. He can have 33 here. Apart from that he can have a ton of combo draw hands (flush draw, straight draw). Idk how I feel about our 4b on flop. When I think of hands we lose to the only one that makes sense is 33. Seems like we're ahead of enough of villains range that getting the money in on the flop seems okay? I could be way off & this is just a gigantic punt. However, villain can have a ton of hands that we are ahead of that have enough equity where villain will get all the money in : JTs, Axhh (any flush draw), KJcc/KTcc (maybe?), AhQx which are all hands we are okay w getting the money in against vs 33 which even tho it sucks we are behind, we still have equity against. Would be interested to see what others think of this spot cause I am not entirely sure I played this correctly.