"Beat" meaning "lame/bad/crappy, etc." existed among a certain group of kids I knew back in the late 70s. I'm mildly surprised that others in the world have also given it this meaning in the 21st century. Although I've never heard any other people use it, those kids might have picked it up from someone else back then. Until I saw this thread, I thought the word disappeared when they did.
As they used it, "You're beat" meant "You're lame/you suck."
If you're talking about how tired someone is, "She's beat" sounds fine. "She's rather beat" sounds a bit odder but still possible. But this context doesn't make it sound at all as though they are discussing the level of tiredness of this person. So it sounds very odd indeed.
I think the slang meanings suggested by Owlman and others work much better.
The quote was also "Thirty five or something." So...which is more likely the meaning here as a motive for mentioning her age at all? She looks tired because of her age, because younger people never look tired or even get tired? or "She looks way too old for me, look at her face, she must be 35 years old."
Well, as near as I can glean from Google Books, that's exactly the context. Nick and Pres have an ongoing context to see who can bring a girl home, using an opening line that relates to financial matters. Nick apparently won on this occasion, and is described as high on cocaine. Immediately after this conversation, Nick tries to sneak the girl out of the house, and her eyes are mascara-stained, presumably from the night before.
I don't know how much this actually helps, but this is all we have about the girl that I can find in the Google preview.