2 hands OOP $3.30+R: Best line?

[Ification]

CO in this hand is one of those LAGG monkey droolers that will try and attack weakness at both oppurtune and inappropriate times. He just stacked a guy: J3 > AJ.
Stats are 43/8/9 over ~57 at the time FWIW
Some will say to fold preflop but getting >5:1 and delicious implied odds it just felt bad to fold.

Tournament, 250/500 Blinds 60 Ante (9 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

Hero (SB) (t17585)
BB (t15820)
UTG (t38370)
UTG+1 (t17254)
MP1 (t14400)
MP2 (t13577)
MP3 (t8947)
CO (t34308)
Button (t30880)

Hero's M: 13.63

Preflop: Hero is SB with 4, Q
5 folds, CO calls t500, 1 fold, Hero calls t250, BB checks

Flop: (t2040) K, 8, A (3 players)
Hero checks, BB checks, CO bets t1500, Hero calls t1500, 1 fold

Here I know he's going to bet, since he's closing out the action and cannot stand to go a street without chips going into the pot. And I think he'll fire most turns.

Turn: (t5040) 9 (2 players)
Hero checks, CO bets t3500,

Again. same reasoning for the check.
Is there any value in a check-raise here (i think hes just aggressive...not stupid) or is this a spot where Ive gotten max value out of worse hands and just hope he's gonna fire a 3rd barrel with a worse flush?

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In this spot i don't want to play it too passively and lose value from AJ and KJ type hands. And can definately see worse hands calling on this board to a check raise or a big lead out on the river. Flop call may be questionable but I find it hard to give min-bets respect if I have nut outs. UTG is fishy doing things like calling down with second pair on wet boards and MP3 is meh, decent.

PokerStars No-Limit Hold'em, $3.00+$0.30 Tournament, 375/750 Blinds 90 Ante (9 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

Hero (SB) (t23070)
BB (t14470)
UTG (t27740)
UTG+1 (t12454)
MP1 (t12925)
MP2 (t69092)
MP3 (t40234)
CO (t17855)
Button (t32320)

Hero's M: 11.92

Preflop: Hero is SB with Q, K
UTG calls t750, 3 folds, MP3 calls t750, CO calls t750, Button calls t750, Hero calls t375, BB checks

Flop: (t5310) 5, J, 9 (6 players)
Hero checks, BB checks, UTG checks, MP3 bets t750, 2 folds, Hero calls t750, 1 fold, UTG calls t750

Turn: (t7560) J (3 players)
Hero checks, UTG checks, MP3 checks

River: (t7560) 10 (3 players)
Hero checks, UTG bets t750, MP3 calls t750, Hero wants to raise but only beats like a few hands that call.

[fjuanl]

1st hand:
so far so good. a turn check/call sets up a nice pot sized river shove. in the 3r I wouldnt want to check the river because so often youll get value from all kinds of heart flushes

2nd hand:
you beat a ton of hands and id rather lead out for 3.5-4k. given how the hand has played out so far (weakly), I expect some people will look you up with Tx, 9x, and of course Jx. As played, your hand is good like 99.9% of the time