She has taught fiction and nonfiction writing at Yale University, Goucher College, the Paris Writers Workshop and elsewhere.
Weber was born in New York City, the daughter of Andrea (née Warburg; 9/29/1922-1/18/2009) and Sidney Kaufman (died 1983).
In 1976, she married Nicholas Fox Weber, cultural historian and Executive Director of The Josef and Anni Albers Foundation and moved to Connecticut.
In 2004 Weber was the artistic advisor for a restoration recording project with the non-profit label PS Classics which resulted in the release of a CD of the complete score, with Broadway performers and an orchestra conducted by Aaron Gandy, of the 1930 hit Broadway musical Fine and Dandy.
In January 1993, the short story "Friend of the Family", her fiction debut in print, appeared in The New Yorker.
In July 2011, a memoir called The Memory of All That: George Gershwin, Kay Swift, and My Family's Legacy of Infidelities, was published by Crown, and in a paperback edition in June 2012 by Broadway Books.
Winner of numerous awards for her work, Weber has been hailed as "a brilliant and ingenious formalist" [2] Her most celebrated book, Triangle, has been described as "a marvel of ingenuity... a wide-awake novel as powerful as it is persuasive"[3]