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|Date of birth||10 July 1984|
|Place of birth||Harthill, Scotland|
|Linlithgow Rose FC|
|Tynecastle Boys Club|
|2006||→Queen of the South (loan)||15|
|2006–2007||Queen of the South||28|
|* Senior club appearances and goals counted for the domestic league only and correct as of 11:40, 21 October 2012 (UTC).
Weir started his career at Heart Of Midlothian, making his senior debut in 2001 in a 3–2 loss against Aberdeen, where he was sent off in the final minute for kicking Robbie Winters. During his Hearts career his goals-to-games ratio was unremarkable, although he is noted for scoring two goals in the last minute of added time against Hibernian in the Edinburgh Derby of 2 January 2003. Hibernian scored two late goals in 89th and 92nd minutes to go 4–2 up. However, the two goals by Graham Weir in the last 42 seconds of injury time marked an even more dramatic comeback by the Hearts, for a final score of 4–4.
In January 2006, Weir was loaned to First Division club Queen of the South until the end of the season. The loan deal was subsequently made permanent and he spent the 2006–07 season with the Dumfries club before joining Raith Rovers in June 2007.
He is the brother of Steven Weir, also a football player.