No, it's not weird if you're not hitting on her. Students and professors do fairly frequently stay in contact, particularly if the age gap isn't huge. Btw, I would carefully read her body language before attempting a hug. Some profs will be fine with that, and some won't.

I have had a few students who seemed to have an interest in me. This is just one of those things that you sort of just know from interactions and body language. A lot of eagerness, a lot of compliments, a lot of e-mails. The stronger you come across, the more likely she's going to be able to sniff something out, for what it's worth.