Passive play Out Of Position = losing chips
First of all, I would like to emphasize that it is essentially almost never profitable to check/call all the way to the river out of position, especially at the micro stakes, unless you have the absolute nuts, and either think your opponent has a hand he's willing to continue hanging himself on, or think that he's willing to continue bluffing. Otherwise you're just bleeding chips while you pray for your outs (I've done it many times myself !) There are some other situations (if you are positive the villain is on a bluff or has a weaker hand he's willing to commit to), but they are much more difficult to identify and navigate skillfully.
Secondly I have to agree with c9 here, I don't think that smooth calling with a marginal hand out of position is a profitable call in most cases. When you have a marginal hand (QJo is definitely marginal), you have to find other ways to make give it strength (i.e. seize the initiative by raising, or make sure you're calling in position). Playing passively with a marginal hand = bleeding chips, in my experience. I don't know that much about small ball, but I do know that the same basic principles still apply (play in position, seize the initiative when you think you have the better hand).
It would seem to me that the only way calling out of position preflop would make sense in this context would be if you plan on being very aggressive post flop if you hit the flop in any way, and suspect his stealing range has missed completely; but you still have to be willing to get out fast if he continues his aggression. Otherwise you're basically praying to hit the flop like a train (top two pair, strong straight draw, etc), and folding otherwise (and middle pair-weak kicker definitely does not qualify as 'hitting like a train'). I would also add that a creative move like this (calling out of position with a marginal hand with the intention of bluffing a late-position stealer) are small ball strategies that generally only work against sophisticated players capable of thinking on a higher level; I've been playing $5NL for a while now, and there aren't too many players like that yet at these stakes.
If you think that his BTN raise is a steal here, you're better off finding out by 3 betting him preflop, before he has a chance to connect with the board; if he 4bets, you can get the heck out of dodge, and if he smoothcalls, you can wait for the flop and see if it might be profitable for you to lead out and scare him off. How you continue will depend on how hard you hit the flop, and how you think his range may have missed the flop, and you must be prepared to give up your play if he continues his aggression by raising.
If he calls your flop bet, you should either give up (check the turn with the intention of folding to any bet) or fire a second barrel on the turn if you think he's capable of folding here. Again, if he raises you on the turn get out, and if he calls, I would again suggest giving up on the hand to any river card that misses you. There's no point in betting the river if chances are you're already beat (2 smooth calls by a preflop raiser is starting to suggest a lot of strength).
All of this continues to be a very risky line in my opinion because you are out of position (especially in a micro stakes cash game, where we really don't get very much for stealing), but still potentially much more profitable than passive play.
Therefore, as played, I agree with you that taking the initiative on the flop and finding out if he was stealing or not would have been more profitable, but still risky for the reasons I outlined above. Another much more risky option would be to attempt a check-raise, showing massive strength. However, I still can think of any number of hands who would have attempted a steal from the BTN that have a K in them (K8-KJ, or Kxs), and because you already showed weakness the villain is probably not likely to let it go to sudden aggression. And if he happened to have KJ or K7s you're really in bad shape. This is in addition to the fact that at $5NL you still have a lot of people willing to go All In with Top Pair-Weak Kicker, and I would suspect that's exactly what he's holding here.
I hope that's helpful to you, best of luck out there!