Daniel's (editor in chief of a fashion magazine) slept with a gril who is 16. And now her mother is trying to get him to put her on the cover of the magazine or she tells the police what happened. He's trying to give them money.
Mother: "This isn't about money. This is about Petra's career. She's going to be the next Kate Moss but not such a piggy."
The line is supposed to show that the mother is a psycho. Not only is she so desperate to get her daughter on the cover that she cares more about blackmail than the fact that her daughter had sex with this guy but she also wants her daughter to be skinnier than Kate Moss who is famous for being skinny even by models' standards.
And for anyone who doesn't recognize the characters' names instantly by now, this is from Ugly Betty. From the discussions I've found using google, it sounds like this mother character is the equivalent of a stereotypical stage mother.