Wedderburn won academy player of the year at Stoke City in his first season at the Potters, playing regularly with the youth team and reserves, he also travelled with the first team during this season but not making the bench. Second season as an academy player saw him take the captain's armband for the season, during this season he was named on the bench in every League cup game but not making his debut. After some impressive performances in Stoke's Academy side which saw Wedderburn sign his first Professional contract at Stoke lasting 1 and a half years. After this, he moved to Notts County on loan. Wedderburn made his league debut whilst on loan at Notts County on 6 December 2008, playing in the 1–0 home win over Morecambe. After extending his loan spell for the second time before 25 January 2009, his loan spell was, once again, extended until 3 March 2009. He went on to make a further 9 league appearances for County before returning to Stoke in March 2009. On 17 September 2009, Wedderburn was called up to the England Under 19 squad three European U19 Championship qualifiers in October 2009. Wedderburn signed on loan for Hereford United in November 2009. After making three appearance, Wedderburn return to his parent club. Wedderburn was released by Stoke at the end of the 2009–10 season.
Northampton Town
Following his release from Stoke, Wedderburn signed for League Two side Northampton Town on a two-year contract. After joining the club, Wedderburn says Manager Ian Sampson was the reason he joined the "Cobblers". He made his debut for the club, on 14 August 2010, in a 1–1 draw with Accrington Stanley. In the second round of League Cup, Wedderburn made assist from the corner to allow Andy Holt equalise against Reading and the match would go in a penalty-shootout after a tie 3–13 in the regular time and kept after extra-time, but in the end, Northampton won 4–3 on penalties. In 2010–11 season, Wedderburn made thirty-seven appearance in all competitions. In 2011–12 season, under new manager Gary Johnson and Aidy Boothroyd, Wedderburn playing time was widely used, as he made two appearance. The main factor was suffering injuries like two sets of ruptured ankle ligaments, a hamstring injury and two calf strains. After making a recovery from an ankle injury, Manager Johnson placed him on loan list to gain first team experience. In January transfer Window, Wedderburn was expected to leave the club, but no avail. Wedderburn was frozen out of the first team by Johnson; instead, spent time on the bench. Wedderburn played his first match since September, in a 3–1 loss against Crawley Town on 17 April 2012. After the match, he thought his Northampton's career had ended, having receiving bad luck in the 2011–12 season and delighted to make his return. In May 2012, Wedderburn was released from Northampton after being told his contract would not be renewed.
Corby Town
On 13 August 2012, Corby Town, and former Northampton Town boss, Ian Sampson announced in a post match interview that he was hoping to secure the signing of Wedderburn before the start of the league season.
Cowdenbeath
In July 2013, Wedderburn signed for Championship side Cowdenbeath after a trial spell. Wedderburn scored on debut in the first round of the Scottish Challenge Cup, in a 3–1 loss against Dunfermline Athletic. Cowdenbeath made his league debut in the opening game of the season, in a 2–0 loss against Greenock Morton. Wedderburn then scored his first league goal of the season, in a 4–2 loss against Hamilton Academical. Wedderburn went to make 40 appearances, scoring two times in all competitions, having played out in different positions from defence and midfield. In the 2014–15 season, Wedderburn continued to be in the first team and captained one match against Raith Rovers on 30 August 2014 before coming off in the 31st minutes, due to an injury. Wedderburn then scored his first goal of the season, in a 2–1 loss against Livingston on 11 April 2015. However, the club was relegated to League One, as he made 34 appearances and scored once in all competitions.
After just one season with Inverness Caledonian Thistle, Wedderburn signed a pre-contract with Scottish Championship side Dunfermline Athletic becoming their first signing of the summer. Wedderburn previously played for Fife rivals Cowdenbeath before transferring to the Caledonian Stadium.
Raith Rovers
In July 2018, Wedderburn joined another Fife club, signing a one-year contract with Raith Rovers with the option of a further year if the club earned promotion from League One.
Airdrieonians
On 10 June 2019, Wedderburn signed for Airdrieonians.He made 17 appearances and scoring in two games against Forfar and Queens Park.
