Cooper was born Marianne Leone in Boston, Massachusetts, to Italian immigrants. She married actor Chris Cooper in 1983. In 1987, their son, Jesse Lanier Cooper, was born. Three months premature, Jesse developed a cerebral hemorrhage and cerebral palsy. After searching for the best schools for children with special needs, Cooper and Leone moved to Kingston, Massachusetts, where they became strong advocates for disabled children.
Leone has had roles in several films, including The Thin Blue Line (1988), True Love (1989), Goodfellas (1990), Household Saints (1993) and The Three Stooges (2012). She has also acted in a small number of television series, including Kate & Allie (1985) and Brotherhood (2007). Her longest-running recurring role was playing Christopher Moltisanti's mother in nine episodes of The Sopranos from 2002 to 2007.
On January 3, 2005, Jesse Cooper died from SUDEP. A memorial fund was set up in his name, the Jesse Cooper Foundation. Leone's memoir, Knowing Jesse: A Mother's Story of Grief, Grace, and Everyday Bliss, was published in September 2010 by Simon & Schuster.
Leone's essays have appeared in The Boston Globe. Her essay "Knitting: Epic Fail" appears in the anthology Knitting Yarns: Writers on Knitting, published by W. W. Norton & Company in 2013.