Weston's first role was in a 1975 episode of Thriller, and parts in Raffles, The Sweeney, The Professionals, Agony, Shoestring and Bless Me, Father soon followed. She also appeared in the video for the 1984 Ultravox hit single Dancing with Tears in My Eyes. Since the late 1980s, she has appeared in The New Statesman, Boon, A Bit of a Do, About Face, Nightingales, Jonathan Creek, Casualty, Emmerdale, My Family, New Tricks and a main role in the 2000 sitcom Pay and Display.