As someone who has liked a TA, I would advise that going after him would not be a good idea. I'm not saying that you can't pursue him just because he's older and not your age because going after older guys is perfectly fine in normal situations (unless you are a minor or he's married). But that's the thing; you don't have a normal situation because he's in a position that has power over you. This power imbalance is frowned upon by many for good reason. For instance, being in a relationship with him would cause some sort of clear cut bias either in your favor (because he likes you) or against your favor (his way of compensating that he isn't picking favorites which then just turns to reverse favoritism which is still bias). This would cause tension within the relationship as well as his standing as a teacher and that won't be good for either of you.
So if you do ever want to be in a relationship with him, I'd suggest waiting until the class is over (assuming you're not a minor) or maybe even until you graduate. I'm not going to tell you that this will be morally right or wrong if you do choose to pursue him later because I'm in no place to judge (mostly since I've been in your shoes and also this is sort of how my parents met). You can do whatever you think is best for you after this but just don't do anything until you guys are no longer teacher and student. Also finals are coming up and you should focus on that for now! (Which reminds me, I gotta get studying....)
Anyway, good luck and I hope that nothing bad will come out of this.