11$; 10man; bb60; AQo, 3way, K22r, cbet?

Grabbed by Holdem Manager
NL Holdem $60(BB) Replayer
SB ($1,920)
BB ($2,670)
Hero ($1,940)
UTG+1 ($1,940)
UTG+2 ($1,640)
MP1 ($2,110)
MP2 ($3,270)
MP3 ($660)
CO ($1,980)
BTN ($1,870)

Dealt to Hero Q♥ A♦

Hero raises to $140, fold, fold, fold, fold, MP3 calls $140, CO calls $140, fold, fold, fold

FLOP ($510) 2♥ K♣ 2♦

Hero checks, MP3 checks, CO checks

TURN ($510) 2♥ K♣ 2♦ T♠

Hero checks, MP3 checks, CO checks

RIVER ($510) 2♥ K♣ 2♦ T♠ 9♦

Hero checks, MP3 bets $520 (AI), CO folds, Hero folds

MP3 wins $510

MP3 fishy unknown 37/11/inf/19
CO BE 'reg' 28/8/1.4/250 fold to cbet 55% (11)

i almost never cbet when miss in multiway pots, but maybe here is a good spot to do that?

my reasoning:
- if i check i may very easily give up the best hand
- if im called im almost sure to be beaten which make it easy for the later streets
- the board is so dry that im almost never called by worse (which has bothe disadvantages and advantages - saves me difficult decisions on later streets)
- there's a slight chance i may get a fold from better hands (mid pockets), especially from the CO

(the disadvantage is that i have to play for stacks with MP3 if he decides to stay in the hand..)

does that make sense? should i cbet here?

as played - should i go for a delayed cbet for the reasons mentioned above + this time we can get called by worse + we picked up a gutshot + we have an even bigger chance to fold out pocket pairs