"The Big C," which premiered Aug. 16, follows a suburban wife, mother and teacher (Linney, of Time Stands Still, The Crucible and "John Adams," among others) who discovers that she has terminal cancer.
"Weeds," which covers a suburban widow (Parker, a Tony Award winner for Proof and Emmy winner for "Angels in America") who becomes a marijuana dealer, will start its seventh season next year.
The premiere episode of "The Big C" garnered the highest ratings for a Showtime series premiere in eight years (6.5 million viewers). The "Weeds" season-premiere ratings (over 6 million viewers) were also a record for the series.