In the river you can either do a value bet or a bluff. Thatīs the main reason of why i donīt 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. Whatīs your propose on that bet? If itīs making more money by getting some callers, thatīs 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, thatīs 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 donīt 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. Thatīs 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 isnīt 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 donīt like being results oriented, so my answer to your first question is no, you shouldnīt be betting more than the minimum. In fact, you shouldnīt 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 itīs 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