The Terras lie 21st in the National League, four points from safety with 23 matches remaining.
Former Doncaster Rovers captain Stock won just 17 of his 69 games in charge of the club.
But the 40-year-old did have a positive impact last season as Weymouth finished 18th on their return to the National League last season, following an 11-year absence.
Former Rovers boss Sean O’Driscoll, who joined Stock’s backroom team in December, has also left the club.
Stock captained O’Driscoll’s Doncaster team to League One play-off glory in 2008.
He was O’Driscoll’s first signing at Rovers, initially on loan, and went on to make 216 appearances for the club.
Stock was appointed Weymouth boss in September 2020 after working as an academy coach at Bournemouth.