Eliza is Patty's best friend in college, who turns out to have an unhealthy obsession with Patty, as well as a serious drug problem. It's also through Eliza that Patty first meets Richard, and thus Walter as well.
Eliza serves a few useful purposes. One is to exemplify Patty's struggles with intimacy (which we discuss more in "Themes: Friendship"). Another is to shed light on the interesting relationship between Walter and Richard. (And guess what? We'll talk about that in "Themes: Friendship" too. See you there.)