I think the major point of contention is whether or not to play the hand at all. My usual haunt these days are the $50 and occasional $100 SNGs, but as many of us have, I spent a bunch of time on lower levels before moving up the ladder. On the $10+1 SNGs, the quality of players is often fairly miserable, so I wouldn't read too much into a $125 raise in EP. In fact, more often I would put this guy on anything from a mid-pair on up. Given this is a $10 and the bet was less than 10% of the stacks, I see no problem playing this hand. Even at the $50s you'll see some weak players make moves like this, so at $10s, I'd practically guarantee it!!
On the flop, you're right to notice that the bet size was on the small-ish side. I'd still be thinking mid-pairs and MAYBE a queen. He could also have a weak K at this point I guess, but with a rainbow flop, whether it's suited or not is currently meaningless and your flop raise should give him cause for concern. When he just calls you on the flop rather than re-raise, I more often than not will take that as a sign of weakness (at the $10 level) since most players with a really good hand at this level will try and get all your chips in one fell swoop rather than suck you in to doing the betting.
Once he checks the turn, I have to agree with the earlier poster, you need to put in another reasonable bet and maybe even push all-in (this latter approach is probably better since it applies the maximum pressure and doesn't give your opponent any option other than fold or call prior to seeing the river card which may or may not help him). I'm guessing that more often than not, you're in better shape with MPTK in this spot.
Of course, like I said, on a higher limit table, that intial $125 means something entirely different. On a $10+1, I put myself in a great spot if I've read this correctly and if not, well then, I'm slightly unlucky and I go find another $10 to play. In a lot of cases, I'd rather try and build a stack early than wait until later when the blinds knock me out in 4th or 5th.