Weldon had a brief television career in the 1950s. Her first appearance in 1955 was in an episode of The Millionaire, starring Marvin Miller. She made three appearances on Lux Video Theater in various roles. She also played Marian Keats in the title role of the Perry Mason episode, "The Case of the Angry Mourner" in 1957. Her final television appearance was in 1958 on Shirley Temple Theater.
Weldon's film debut came in the 1953 film The System. Although her background was singing in operas, The System and her next two films, So This Is Love and Rear Guard, all had her in non-singing roles.
She became a contract Actress with Warner Bros. where she remained until her contract ended in 1954. Her most prominent film was the cult thriller Them!
In 1955, Weldon was one of the regular Singers on the syndicated program This Is Your Music.
She sang at the opening of the New York State Theater at Lincoln Center, in 1964.
After working in film and television, she resumed her career as a singer in road company productions including The Music Man and Oklahoma!. Weldon retired in 1980.
