QQ in in a 3bet 3man pot

[BigBadBull]

Effectively we are 200BB deep, dynamic of the table has been off the walls, a lot of 3betting and shoving(with good hands, but that's if villain is paying attention) preflop. Villain is the mark at the table(total donk, folds very low % of time on any street, plays around 80% hands.

With so many people in, even in 3bet pot I can not just call and let them see the flop which can have plenty of scary cards for me vs. his range. What my 4bet is trying to accomplish is to get the money in preflop or let him fold his Khigh suited or whatever he's playing.
Any comments on the hand appreciated, mostly Im unsure about my 4bet sizing, what would be a better size, and what reasons are there NOT to 4bet.

$0.25/$0.5 No Limit Holdem
5 players
Converted at weaktight.com

Stacks:
UTG kcools ($20.75)
CO Hero ($165.40)
BTN PokeyReese ($49.25)
SB Trafalgar ($49.50)
BB Kmizzy100 ($99.95)

Pre-flop: ($0.75, 5 players) Hero is CO :Qc: :Qh:
kcools calls $0.50, Hero raises to $2.25, 2 folds, Kmizzy100 raises to $7, kcools calls $6.50, Hero raises to $32, Kmizzy100 folds, kcools calls $13.75

[ATOTHEC101]

i like it, kmizz's range is far weaker than yours and ideally you want to isolate the shorty rather than play 3 way with a vulnerable hand against a guy whos 200bb deep as well as the shortstack. Also this 4 bet helps alot in defining kmizz's range though i definitely wouldnt 4 bet this much unless your happy getting it in if kmizz calls, id 4 bet to 22 myself to give you some breathing room postflop as raising this much gets the shorty all in regardless and also gives you some room for manouver if called by the bigstack.

[BigBadBull]

ok second question arises because I had some1 else saying i should bet smaller as well because then Im able o fold the hand.

The whole reason for such large 4bet is to get all the money in prefop, but now Im starting to question that. Should I really be ready to fold QQ against 84/4 villain 200BB deep?