Bet Sizing Help - Turning a Straight

$10 monster stack tournament early on, 15k starting chips blinds 20/40

Villain early position raises to 120 I call MP with 89s LP calls three to the flop, 420 in the middle.

Flop comes TJ4 rainbow giving me the open-ender. EP opens for 200 both players call. 1020 in the middle to the turn.

7 turn, giving me the semi-disguised straight. EP opens for 440 I reraise to 950 LP folds EP calls. Head-up to the river with 2920 in the middle.

River is a K. Villain checks. The only hands that beat me are AQ and Q9. Neither seem particularly likely to me. Villain flatting the turn and checking the river makes me feel like his hand isn't particularly strong. Villain and hero each have around 13k behind.

How do I size my bet here? I feel that my hand is good but villain is representing enough strength that I don't need to make a thin value bet. I bet 3100, a little larger than the pot. Villain snap calls then mucks. I take down a decent little pot.

My question here is if I should've bet harder on either the turn or the river. I'm obviously happy with the hand result but can't shake the feeling that I might've left some chips on the table. I was a little worried about too strong of a re-raise on the turn scaring off EP, but given that villain probably isn't thinking about the straight I may have underbet there, which obviously costs me even more value on the river.

Preflop
Since you are almost 400BB deep, I guess, its ok to make this kind of speculative call with a hand, that can win a big pot against an overpair. With more normal stacks I prefer a fold.

Flop
I would at least consider raising the flop. You have a bucket of equity, but right now you only have T high, so whatever you get people to fold, its good. By raising now you are also building the pot, so you can get paid, when you improve, or apply maximum pressure when you dont.

Turn
I like raising with the nuts obviously, but I think, your size is way to small. Pot is 1.900, after you call his 440 bet, and you only make it 510 more to go. This means, you are betting just 25% of the pot, and you dont need to give him such a great price to get action. Its almost like, you are begging him to stick around and potentially draw out on you.

River
AQ is certainly a hand, he can have, and you also have a lot of chips left behind. Which put you in a somewhat precarious spot, if you get check-raised. I am less worried about Q9, since he opened UTG, but there are 16 combos of AQ, so this is not the greatest card for you. For that reason I probably dont go for the very polarized overbet but rather something more normal like 2/3 pot.

Conclusion
I think, you need to put in more chips early on but hold back just a little on the river.

I agree that turn sizing should be much larger.

General rule of thumb: Bet/raise sizes should be higher on coordinated boards. If you're raising here (which is a good option), I would go at least 1400. While I wouldn't normally make this play, even jamming is far from crazy here; there are many worse hands that can call here, but might be scared off at the river.

Your river sizing is probably a bit big but you do get paid off big with a non-nut hand, so nice work getting max value

Great answers from fundiver and Colin. In particular, Fundiver's analysis of the turn bet stands out for me. I say that because I have played a hand or two that played out almost exactly like your example. What I am trying to do now is recognize when I am acting too fast. I think reacting a little too quickly was my downfall on the turn. Now I try to slow down all my actions and pay attention to one piece of info on the screen that I was ignoring...the pot size. Like fundiver pointed out the turn raise was too small in relation to the pot and gave the other guy a good price. What I wasn't doing in my hands was thinking how my actions affected my opponent....a 2nd level of thinking that was missing from my game.