What is the exposition of "The Fat Girl"?

"The Fat Girl" is a short story by a master of the form, Andre Dubus. The title refers to the protagonist, Louise, and the story covers her experiences from childhood through adulthood. It's worth noting that that term "fat girl" describes how Louise sees herself (and how the people around her, especially her mother) view her when she is young. By the time Louise is a young adult, she's not heavy anymore. But she still views herself as a fat girl, even when she is in a slender body that she's worked hard to earn and maintain.
The fact that Louise's struggle with her weight will continue throughout the story is why the exposition is so important. We have to understand the protagonist's background to properly understand the rest of the story. Dubus doesn't waste any time in establishing this. In the second paragraph of the story, he reveals key details of Louise's childhood:

It started when Louise was nine. You must start watching what you eat, her mother would say. I can see you have my metabolism. Louise also had her mother’s pale blond hair. Her mother was slim and pretty, carried herself erectly, and ate very little. The two of them would eat bare lunches, while her older brother ate sandwiches and potato chips, and then her mother would sit smoking while Louise eyed the bread box, the pantry, the refrigerator.

In this passage, we learn plenty: Louise's mother is extremely image-conscious. Even though she is "slim and pretty," she worries that Louise will have weight problems. (We can't know whether or not Louise's mother was ever actually overweight, and that's part of the problem: is this problem about perception, or is it a real health concern?)
In the exposition, we also learn about Louise's father, who is kinder and more sympathetic to his daughter:

Her father was a lawyer and made a lot of money and came home looking pale and happy. Martinis put color back in his face, and at dinner he talked to his wife and two children. Oh give her a potato, he would say to Louise’s mother. She a growing girl. Her mother’s voice then became tense: If she has a potato she shouldn’t have dessert. She should have both, her father would say, and he would reach over and touch Louise’s cheek or hand or arm.

The story will go on to describe Louise's experiences in high school and, later, as a young woman entering the spheres of dating, marriage, and motherhood. But we'll see how Louise's judgmental mother and kindhearted father, and the interactions they have with their young daughter when she is nine years old, will shape the way she sees herself in the future.