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What do you put him on when he check raises?

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That's just about it. Calling it needs a good reason, and the reason was the 2x raise (I don't think the 2x raise is generally a bad play but it depends, if one can get $12 with little risk and maybe $20 on the turn, considering milking and limit holdem comparable odds for taking the chance of a suckout, it being better than the opponent folding), but considering the check raise and the board type vs. the preflop raiser, small blind cold call, and likely a more solid brand of a game (than e.g. 400nl) and having just an MP with a weak kicker that one could in cases fold even in limit games, if not putting the opponent on a bottom pair or a draw.