serious about (someone)
Wanting or committed to a permanent or long-term romantic relationship with one. I know he's getting really serious about her. I wouldn't be surprised if he proposed in the next year or two. I don't really want to get serious about anyone during my time in college. I'd rather be free to do as I please.
serious about someone
in love with someone; romantically interested in someone. I'm afraid I'm getting serious about Bill. Bill, unfortunately, is pretty serious about Mary.