Wight started his career with Arbroath in 1997, before leaving in 2002. He spent time at the Kentucky-based Lindsey Wilson College and Tennessee-based Cumberland University in America, before returning to Scotland to play for Livingston. He then returned to Arbroath in 2007,before joining East Fife in the January 2008 transfer market.
After a short career break, in which he returned to the Lindsey Wilson College to assume the position of assistant manager,Wight returned with First Division side Raith Rovers, but failed to make an appearance before joining fellow First Division side Cowdenbeath, initially as a goalkeeping coach. Wight made two appearances during his time with the Cowdenbeath-based side.
After a short spell with lower division side Berwick Rangers as a player-goalkeeping coach, Wight moved to Finland to join Veikkausliiga side IFK Mariehamn in 2016, while also working as a goalkeeping coach and assistant manager for Kakkonen side FC Åland. He was named interim manager for the end of the 2016 season.
Returning to the United Kingdom, Wight joined Carlisle’s coaching staff in 2018, before venturing southbound to join Darren Sarll’s coaching staff.