Born and raised in Spartanburg, South Carolina, Weston might have ended up as yet another Southern matron had not her father passed away. Believing he would have disapproved of her career choice and her move first to London to study and then to NYC to pursue acting, Weston originally enrolled in college as a psychology major. By the late 70s, though, she was marking time as a waitress in Manhattan while seeking her big break. Following stints at regional theaters, Weston finally made it to the Great White Way alongside Kevin Kline in 1979 in Michael Weller's play "Loose Ends". She then co-starred with Irene Worth in Edward Albee's "The Lady From Dubuque" before finally succumbing to the lure of the great salary on "Alice". ("I kept turning it down until the money became so phenomenal that I just had to do it.").

While there was an invisible barrier between TV actors and film actors at that time in the early 1980s, Weston contented herself on playing the good old Southern gal, spouting aphorisms. She wisely kept a low profile (and pursued a romance that ended badly) when the series ended its run, gradually emerging as a character actress in 1988's "Stars and Bars" and "A New Life". After a turn as Adam Horovitz's rather unpleasant mother in "Lost Angels" (1989), she went on to appear in "Little Man Tate" (1991) and made periodic forays into theater. 1995 saw her deliver a superlative dramatic turn as the mother of a murdered child in "Dead Man Walking" and the following year, she reminded audiences of her finely-honed comic capabilities playing a spirited woman Ben Stiller believes may be his birth mother in "Flirting With Disaster".

Weston won critical praise and a Tony nod for her featured turn as a Southern matron in Alfred Uhry's "The Last Night of Ballyhoo" in 1997. She had pivotal roles in several 1999 releases, playing the wife of a Civil War-era farmer in "Ride With the Devil", Cate Blanchett's snooty aunt in "The Talented Mr. Ripley" and the bitter Germanic mother of a fisherman thought to have been murdered in "Snow Falling on Cedars". Stanley Tucci tapped Weston to play the efficient secretary/receptionist at he New Yorker in "Joe Gould's Secret" before the actress returned to Broadway as the matriarch in the highly-praised staging of Sam Shepard's seminal "True West" (both 2000).