What the sentence means is that she is very excited about the weekend, she wants the time to pass quickly, and she wants the weekend to come very much.
But the word choice isn't very good.
You wouldn't anticipate the weekend, you'd wait for it.
You are right, Elif, that the sentence means that she is excited about the week-end, she is looking forward to it. But you are wrong about the word choice "...eagerly anticipating the week-end" is very good English, and describes very clearly the feeling of looking forward keenly, rather than just "waiting".