Weaver was of North Luffenham, Rutland, and was admitted a freeman of Stamford, Lincolnshire on 25 October 1631. From 1643 to 1644 he was judge-advocate to the army of the Earl of Manchester.[2] In 1645, Weaver was elected as Member of Parliament (MP) for Stamford for the Long Parliament.[3] He became one of the recognised leaders of the Independents and remained in the House of Commons after Pride's Purge, although he refused to sit as one of the judges in the trial of King Charles I. From 1650 to 1653 he was one of the Commissioners for the government of Ireland. The officers of the Irish army petitioned for his removal on 18 February 1653 and on 22 February he was allowed to resign at his own request.[2]