In the river you can either do a value bet or a bluff. That´s the main reason of why i don´t like betting in the river with medium strength hands. Generally, if you bet in the river you are going to be called or raised by a better hand or your opponent is going to fold with a weak hand. If you analize that, there is no point in betting with a medium strength hand. What´s your propose on that bet? If it´s making more money by getting some callers, that´s pretty of difficult, because you need to be called by someone who holds a worse hand 6s. If you want to make your opponents fold with better hands, that´s nearly impossible with that bet. As Paulsson said, someone with 7s probably would have checked-call there.
So why did you win money with that move? First of all i would like to know what was the buy in of the SNG. On that play, it happened the opposite to one of the reasons of why i don´t like betting in the river with those hands. You were called by an opponent who had a worse hand than yours. Actually, he called with nothing. That´s pretty strange, unless you were playing low buy in. The only reason i may find of why your opponent called, is that he paid to obtain information.
In my opinion a check would be a better play there. Yes you won $50 more, but for me that isn´t worth enough compared to the risk of being called or raised by a better hand or just make your opponents fold and obtain the same as a check. You said that you have won lots of pots like that, but i don´t like being results oriented, so my answer to your first question is no, you shouldn´t be betting more than the minimum. In fact, you shouldn´t be betting there.
Now in relation to your second question, i think that if the turn showed a 6 instead of a 7, then yes, it may be a good time to bet there. You hold second pair and in the flop everybody checked. Now in the turn the SB checked and it´s up to you. A 1/2 pot bet should be enough to see where are you standing or to take the pot right there.
p.s: Long time ago i made a thread abour river betting. You can read it
here.