Her fiction debut in print, the short story "Friend of the Family", appeared in The New Yorker in January 1993. Her short fiction has also appeared in Story, Redbook, Southwest Review, Gargoyle, The Connecticut Review, the Vestal Review, SmokeLong Quarterly and elsewhere. Her short story "Sleeping", originally in Vestal Review and anthologized several times, is being made into a short dramatic film by Group-Six Productions. Her first novel, Objects in Mirror Are Closer Than They Appear, was published in 1995. She was named by Granta to the controversial list of 50 Best Young American Novelists in 1996. Her second novel, The Music Lesson, was published in 1999 and has since been translated into thirteen foreign languages. Her third novel, The Little Women, a Finalist for the Paterson Fiction Prize, was published 2003. All three novels have been named Notable Books by The New York Times Book Review. Her fourth novel, Triangle, which is about the Triangle Shirtwaist Factory fire of 1911, was published in 2006, won the 2007 Connecticut Book Award for Fiction, and was a Finalist for the Paterson Fiction Prize and the John Gardner Fiction Book Award. Triangle was also longlisted for the 2008 International IMPAC Dublin Literary Award. Her fifth novel, True Confections, was published by Shaye Areheart Books in January, 2010. Her literary essays have appeared in numerous recent anthologies. She is under contract with Crown for a memoir, The Memory of All That.

Weber was elected to a term on the board of the National Book Critics Circle, serving from 2001 to 2003.

She has written book reviews, essays, and columns for several publications, including the Boston Globe, the Chicago Tribune, The London Review of Books, The Los Angeles Times Book Review, New Haven Register, The New Leader, The New York Times, The New York Times Book Review, Publishers Weekly, Vogue and Washington Post Bookworld.

Weber has taught fiction writing at Yale University, Goucher College, the Paris Writers Workshop and elsewhere, and she is currently a graduate thesis advisor in the writing program at the School of the Arts at Columbia University.