I would have raised the turn. You are calling the turn bet, with overpair and 3 outs to the nuts. You will not fold the aces getting 13 to 1 on river. So before you initially called the turn you already knew you were going to invest 2BBs to see the showdown, Raise and put your 2BB in now. You have a small amount of fold equity because you raised preflop and AK(a likely holding for you) already has the nuts. You might just win the pot here.

If you get called here you'll probably get checked to at river and now you have a freeroll. If you hit your King you can bet out again with the nuts. Otherwise you can bet again or you can check. Notice that if you check, you have invested the same amount to see a showdown(2BB), except this time you got to put in a semi-bluff. This is definately +EV.

If you get 3bet at turn, you are probably behind, but you will have odds on your straight draw so you have to call(12 -1 [or 14-1 if it is still 3way]). At this level SB could have a number of hands but will likely have 2 pair or better. If you knew his tendencies you could narrow it down alot more and even be comfortable folding the river if you don't improve. On river you will either be getting 15-1 or 17-1. Tough to fold aces in this spot for such good odds. again a situation were it really helps to know your opponents. Call and hope for the best. Sometimes you will be up against donks and win a huge pot you thought you should have lost.

I think the best play would have been to raise flop.