Miriam Linna, founder of Weiss' label, Norton Records, said Weiss died on Friday in Palm Springs, California. No cause of death was given.
The Shangri-Las, formed in the New York City borough of Queens, were made up of two pairs of sisters: Weiss and her sister Elizabeth "Betty" Weiss, along with twins Marguerite "Marge" Ganser and Mary Ann Ganser.
They met in school and as teenagers began performing at school dances and teen hops.
After producer Artie Ripp signed them to Kama Sutra Productions, the Shangri-Las found enormous success as a girl group with a tough, working-class image and drama-filled songs of teen dreams and heartbreak that consumed mid-1960s radio waves.
Their name came from a restaurant in Queens.
Their first hit, Remember (Walking in the Sand), reached the Billboard top five in 1964 for Red Bird Records.
Weiss was just 15 when it charted. The song, which Aerosmith would later cover, was written by Brill Building pop songwriter-producer George "Shadow" Morton.
Morton would be a key architect of the Shangri-Las, developing a sound that fused a Ronettes-style R&B with big teenage emotions.
Leader of the Pack, co-written by Morton, was the top Billboard single of 1965.
On it, Weiss sang: "My folks were always putting him down/ They said he came from the wrong side of town/ They told me he was bad, but I knew he was sad/ That's why I fell for the leader of the pack."
The Shangri-Las didn't last long, disbanding in 1968 amid legal issues, but they remained a pioneering all-female group.
"I truly believe a lot of men were considered artists, whether or not people wrote for them where women were considered products," Weiss said in a 2007 interview at the Rock & Roll Hall of Fame.
After the break-up, Weiss moved to San Francisco and fell out of the music business.
For years, she worked at an architectural firm.
It would be four decades before Weiss recorded an album of new material again.
She made her solo debut with the 2007 album Dangerous Game.
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