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I'd push. If you don't, what's your plan for getting all the money in, pushing the river? Being out of position, I see the turn 3-bet as the better choice. There's just too many cards that can either a) beat you, or b) kill your action on the river. Reraising a trivial amount never appealed to me, as it's clear to any smart opponent that all the money is going in to see a showdown, but a drawing hand isn't forced to pay all the money since on 5th street he already knows his fate.
With villain's raise, pot size is up to $640. You have to put in $700 more if you push, putting the pot size up to $1340. With $550 behind, villain is getting nearly 2.5 : 1 to call here. I think villain calls here with a pretty wide range, making your decision pretty easy.
Another thing you may want to consider is what villain is thinking about you. He raises with 2 limpers in front. Solid LAG calls from the SB which will probably become a multiway pot. Range for you is wide. You check the flop (you are the most likely to check a huge hand here, but that's a different story), other 2 check. Lots of weakness going around. You lead out, probably taking a stab at the pot, and he fires a large bet at you. Either he has something big, perhaps a big draw (if it's even possible to have a big draw when a lot of money goes in on the turn), or he doesn't have anything and you aren't getting anymore money from him. His check-behind on the flop could mean many things, from simply slowplaying a huge hand, to having something but wanting to moderate the pot size on a pretty drawless board, to genuinely having a weak hand that he doesn't want to c-bet against 2 opponents here.
In any case, I think a push is the best play here hands down...
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