One thing I forgot to mention about the turn bet, that ran through my mind at the time I made it:
I'm 75% confident in my pre-flop read of a modest pair, but the 25% uncertainty mostly deals with weak overcards: KQ, Ax. It's possible he limped one of these hands and then tried to punish me for what he perceives as stealing (bear in mind, this is my first active hand at this table, so of course he's going to assume my raise is bogus).
If he does have something like KQ it's the same situation for me as a lower pocket pair, except he has far more outs - so I want to bet the turn to make him pay for his draw. If he has Ax, he actually has a better hand than me, but his flop line still makes sense because he suspects I have a better ace and he's in trouble. So backing it up with a healthy turn bet is a good idea because there's no other way I'm going to win this pot. For reference, see the hand Danneman played in the WSOP last week. He came in for a raise with queens, and was called by KJ. On a king high flop he bet and his opponent called OOP. On the turn an ace came down; he bet again and the opponent folded. Now it's probable that the ace helped form his opponent's opinion of why he needed to fold this hand, but even without the ace, another bet from Danneman on the turn represents a strong hand: probably aces or AK, maybe KQ. This is the only way at this point to make your opponent lay down a better hand than yours that they are still uncertain about.
Now in this hand, I have no fold equity on my opponent if I check behind on the turn, no matter what he has. I am 75+ % sure I am ahead with the nines unimproved, but the 25% of the time I am wrong, I don't mind giving myself another way to win the hand. And if I'm right and he has something like eights or sevens, this is just a value bet that I want him to call. It serves a nice dual purpose.