Poker Good Fold?

PokerStars - 1400/2800 Ante 280 NL - Holdem - 9 players
http://www.pokertracker.com

MP (MP): 53.86 BB (VPIP: 18.82, PFR: 16.67, 3Bet Preflop: 12.12, Hands: 85)
MP+1 (MP+1): 37.67 BB (VPIP: 25.00, PFR: 15.79, 3Bet Preflop: 12.50, Hands: 20)
MP+2 (MP+2): 12.92 BB (VPIP: 11.25, PFR: 8.86, 3Bet Preflop: 6.90, Hands: 82)
CO (CO): 21.27 BB (VPIP: 20.99, PFR: 11.25, 3Bet Preflop: 0.00, Hands: 82)
BTN (BTN): 12.13 BB (VPIP: 22.64, PFR: 19.61, 3Bet Preflop: 0.00, Hands: 54)
SB (SB): 22.09 BB (VPIP: 18.32, PFR: 7.87, 3Bet Preflop: 0.00, Hands: 132)
BB (BB): 18.69 BB (VPIP: 10.34, PFR: 3.45, 3Bet Preflop: 0.00, Hands: 29)
UTG (UTG): 23.43 BB (VPIP: 13.33, PFR: 11.90, 3Bet Preflop: 0.00, Hands: 45)
Hero (UTG+1): 27.93 BB

9 players post ante of 0.1 BB, SB posts SB 0.5 BB, BB posts BB 1 BB

Dealt to Hero: KcKh

fold, Hero raises to 2.05 BB, fold, fold, fold, CO calls 2.05 BB, fold, fold, fold

Flop (6.5 BB, 2 players): Jh 9s 7h
Hero bets 2.21 BB, CO calls 2.21 BB

Turn (10.92 BB, 2 players): Js
Hero checks, CO checks

River (10.92 BB, 2 players): Qc

Hero bets 6.36 BB, CO raises to 16.91 BB and is all-in, fold

CO wins 23.64 BB


This is a hand from the 5.50$ Mini Marathon already in the money, I'm not quite sure how many players remained, but I think it was like about 500 players out of ~5500. The hand left me with a short stack and I had to go all-in shortly after, where I busted the tournament.

So the first question I think would be if I made the correct play by folding.
On the River I bet to get value from maybe hands that hit on the flop but didn't improve on the turn or river and hands like AQ, KQ, QT and maybe even Q9s Q8s if he calls those preflop or hands like TT or 88 if he thinks I'm bluffing in that spot with a missed draw.
But Villain shoves, so at that moment I though he might have had Jx, that he checked the turn with, but after reviewing the hand I was pretty sure he would never check Jx (except J9s, even though Villain could certainly raise that hand on the flop) on the turn as there are too many flush draws and straight draws on the board. So the only hands that are left, are either bluffs or 99, 77, J9s and KT (maybe also QQ, but I'm pretty sure he would 3Bet that hand, maybe not though as he has a 0% 3Bet frequency, but maybe only because he hasn't gotten any premium hands)(maybe even T8s, but I'm not sure he would call that preflop against a UTG+1 raiser and because I had a pretty tight image, that's if he had a HUD or noticed that). The question is if he ever bluffs in this spot, I think if he had a flush draw, either a flopped one or a turned one, he would bet the turn after me showing weakness, and then would bluff shove the river. Anyways, I think any way I look at it, Villain has way more combos that beat me than he has bluffs, if any.

The second question is if I should have played that hand entirely differently.
On the flop I of course bet for value but I think I could have made the bet a bit larger, instead of 33% pot, something more like 45% pot, or even more, because there are so many drawing hands that will call, and of course hands with a Jack.
On the turn I check (at that moment because I didn't want to scare off hands with a 9 or 7 and to not make the pot to big for the case that villain had a Jack), thinking back, I think it would have been better to bet on the turn, because all of the drawing hands would still call. Maybe a 55% pot Bet, or even bigger. When Villain checks back the turn, I was pretty sure I had the best hand and the river was a blank, at least for the flush draws, so I decided to bet for the reasons I state above in the second paragraph. I could have checked the river and induce bluffs from missed draws, which in hindsight would have been I think a better play, but also maybe a lot more costly, as I would have probably even called a shove then.

ps: After writing this post and remembering the 'tells' ( in terms of timing and the type of player he seemed ) I got from Villain and putting all the information together, I think the most likely hand that he had is KT.

Also, why did the Images for the cards not work in the post? Did I copy the Hand wrongly from PT4?

I would really appreciate any comments, tips on the hand and how I could have played it differently or criticism of my play and thinking process.

Thanks!

Source.