Hello there, i would like to get some feedback on the following hand, that i played on level 2 of a 20 player live sit´n go style tournament. The game is relatively loose and splashy, with many limps.
Blinds are 200/400, effective Stack is 22k.
Hero has AThh on the Button, with 4 limpers in front. We think we would have to raise pretty big to get anyone out, so we limp behind.
Flop is 10 2 3 rainbow, with one heart. BB bets 800 and gets 3 calls, we raise to 3000. Everybode folds except for a loose, competent Player in Middle Position, who calls.
Heads up to the Turn, wich is is the 5h, Villain checks, we would check back most Turns, but since we picked up the nut flush draw, we bet 4000. Villain raises to 9500, we call.
River is the Ac, Villain shoves. We kinda hate it, don´t think villain has much bluffs or worse two pair here, but we call off our remaining ~10k for the ~40k pot, obviously we see 46 for the straight.

So, did i missplay this completely? In retrospect, i think raising bigger on the flop and checking back turn, calling a normal sized bet on the river would have been better. As played, can we ever fold the river?

Definitely raise ore because you can't say this was a competent player then tell us he called a raise with 46. Since you didn't raise it's possible he is still competent.

Also:

You should just be calling on this flop and checking the turn for pot control.

Limping on the button with almost any hand is bad in my opinion.

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So raise big.

If you raise, raise bigger. If I did the calculations right, your raise is around 1/3 pot. Not nearly enough to deny anyone their equity with the kind of hands that can outdraw you.

Picking up the NFD is a reason to check back, not to keep firing, in a situation where the villain is only going to check-raise you with hands that beat you. In a limped pot after my flop raise is called I'd be more wary of villain's range, whereas if we bombed it preflop and got called and called again on the flop we're probably at a point we can just put it in.

Yeah, I mean, you're probably screwed on the turn but once you get here I dunno what else you can do. Given the way the table plays is there a 20% chance villain has some worse two pair? I guess.

Make a significant raise preflop. As played, raise the flop bigger if you're going to raise at all, and don't bet the turn.