Born in Los Angeles, but raised in Phoenix and then San Francisco, Meriwether attended George Washington High School with Johnny Mathis. While attending San Francisco City College, she was nominated by a fraternity as Miss San Francisco, won that title, as well as Miss California, and then Miss America. (Although the latter title was bittersweet as her father passed away shortly before she won.) After serving her term, Meriwether joined "Today" and also had her first TV acting job on an episode of "Philco Playhouse". She continued guesting on TV until 1960 when, for two years, she played the wife of an astronaut on the CBS daytime drama "The Clear Horizon". Meriwether then returned to L.A., where she was a regular on "The Time Tunnel" (ABC, 1966-1967) playing a scientist trying to help James Darren and Robert Colbert return to the present day. In 1971, Meriwether was wife to Andy Griffith on "The New Andy Griffith Show" (CBS).
Meriwether had been teamed with Griffith in the feature "Angel in My Pocket" and was impersonating a man when her character was killed by Kim Novak in "The Legend of Lylah Claire" (both 1968). She also portrayed Rock Hudson's wife in "The Undefeated" (1969), her last big screen appearance to date. In addition to TV and films, the actress worked frequently on stage throughout the USA but did not make her NYC debut until joining the Off-Broadway audience participation show "Grandma Sylvia's Funeral" in 1998.