Graham Weeks played for Exeter City between 1976 and 1978. He joined the club as an apprentice and briefly played for Bournemouth before enjoying a long stint with Exmouth Town. He was a member of the Exeter team that won promotion in 1976/77.

He signed for the club as an apprentice on leaving school in 1974 became a full time professional in March 1976. Only nineteen when Exeter won promotion, he made his debut at Colchester United on 4 September 1976 and made 37 starts - together with three appearances off the bench - and contributed one goal against Rochdale. 

Playing a second season - when he only made a dozen starts - he left for AFC Bournemouth where he only played a handful of games. Switching to the Western League initially with Bideford, he then enjoyed considerable success in the strong Exmouth Town side of the early 1980s. Sustaining a knee injury whilst playing cricket effectively ended his football career and, remaining in the Exeter area, he later worked as a technician for BT.