I was out with a girl for a lunch date / party with her friends, and noticed every time I laughed or sighed she would too, and every time I sipped my wine she wouldn't let me do so a single time without in almost perfect unison, picking up her glass of red and drinking until I put my glass down. We might meet up next week and I'm wondering if she's into me?
It's called mirroring. It's a form of body language that indicates romantic/sexual interest or a very strong interest in whatever it is you are talking about or a very deep bond of trust.
You can safely eliminate the third option if you don't know her well. You can eliminate the second option if you weren't doing the talking. But there's always a chance it was coincidence and you should always look at multiple signs and the context.