Last night I played this hand and got in a very uncomfortable spot OTR. I would like to know what you would do and why. Some thoughts I had are in blue.

Scenario:
Late Reg. was still going on. Assume we have no reads on V. BB had closed his PP app I think, snap folded everything pre or time-banked into a check/fold.

partypoker, $0.10 + $0.01 - Hold'em No Limit - 900/1,800 (225 ante) - 8 players

Player5 (UTG): 193,293 (107 bb)
Player6 (UTG+1): 155,275 (86 bb)
Player7 (MP): 31,370 (17 bb)
Player8 (MP+1): 144,271 (80 bb)
Player1 (CO): 76,179 (42 bb)
Hero (BU): 141,556 (79 bb)
Player3 (SB): 81,175 (45 bb)
Player4 (BB): 4,876 (3 bb)

I did consider 3-betting here as a bluff, but we don't have any reads on villian.
Pre-Flop: (4,500) Hero (Hero) is BTN with K♣ J♥
4 players fold, Player1 (CO) raises to 4,500, Hero (BU) calls 4,500, 2 players fold

Flop: (13,500) 4♥ K♥ 9♣ (2 players)
Player1 (CO) bets 6,750, Hero (BU) calls 6,750

I probably should have raised for value here. We usually aren't going to get much value from FD's when they miss OTR however they might still call us off on the turn. Also FD's with a pair like the AKh are going to have to pay us off. However if villian jams after we raise we are in a really tough spot.
Turn: (27,000) J♠ (2 players)
Player1 (CO) bets 13,500, Hero (BU) calls 13,500

And here I had no idea. We get a good price so I'm leaning more towards a call, but I'm really not sure.
River: (54,000) T♠ (2 players)
Player1 (CO) bets 27,000, Hero?

Raise turn is the best choice imo, river is tough, I think we can call since we need to win 33% of the time and there aren't many Q combos in Villain's range except for QTs. We block KQ and QJ

Why didn't you just jam the turn?

Theagent77, Aren't we even getting 25% pot odds since it's a half-pot bet? So if you say it's a call at 33% then it's definetly a call at 25%. Also I called it of and he had KQ of spades. Just wanted to check if it's still a good call given we also call the turn.

killer_kill, Aren't we a little too deep to shove here? Despite that it looks really good. We get massive value from worse kings and at these stakes we might even get some FD's to call.

Not with effective stacks. Villain has like 50k left on the turn with pot being 40k.

Oh yeah you're right was only looking at my own stack, thanks!