Metzger is the dashing and super-hot co-executor of Pierce Inverarity's estate, a lawyer who works at Warpe, Wistfull, Kutitschek and McMingus.
Oedipa first meets Metzger at a hotel called Echo Courts in San Narciso. The two of them watch a film, Cashiered, that Metzger starred in when he was a child actor known as Baby Igor. Metzger works hard to get in Oedipa's pants, and eventually persuades her to play a game called Strip Botticelli (take off a piece of clothing every time you ask a question) that leads to the two of them beginning an affair in Echo Courts.
Throughout the rest of the novel, Metzger basically functions as a tag-along. He goes to The Scope bar with Oedipa and argues politics with Mike Fallopian while Oedipa tries to get information about the Tristero. He also accompanies her to Fangoso Estates, where they bump into his lawyer friend Manny Di Presso.
Late in the novel, Oedipa returns to Echo Courts and learns that Metzger has run off with the young girlfriend of the counter-tenor in the Paranoids. She realizes that their affair meant nothing to him.
When considering the character of Metzger, it is most important to realize what Metzger is not. Since he is a lawyer, you might think that he'll be Oedipa's guide through the complicated business of executing Inverarity's estate. Nope. Instead, he's essentially useless from a legal point of view and is way more preoccupied with sleeping with Oedipa.
After their affair begins in Echo Courts, we learn that Inverarity was all about their tryst, warning Metzger that Oedipa "wouldn't be easy" (2.110). As usual, Oedipa is left to be taken advantage of by the unreliable dudes around her.
So what does Metzger do? He exploits. He is a narcissist who talks endlessly about his film career without once asking about Oedipa. In their relationship, he offers her zero emotional support. It seems that his only concern is sex, a view that is supported by the fact that he runs off with a younger girl as soon as he has the opportunity. All things considered, it seems fitting that Metzger is the German word for "butcher."