Born in Doncaster, South Yorkshire, Weaver played as a central defender and began his career as an apprentice with Sheffield Wednesday and made his professional debut during a loan spell with Doncaster Rovers in February 1997. Released by Wednesday, he moved into the non-league circuit with first Ilkeston Town and then Nuneaton Borough. In the summer of 2002, he made a return to the Football League, signing for Lincoln City, who were managed by Keith Alexander, his former boss at Ilkeston. He signed a new one-year contract in July 2004, but lost his place in the Lincoln team at the start of the 2004–05 season and was transfer listed at his request. Following a loan period at Macclesfield Town, he joined Kidderminster Harriers, and was one of ten players released at the end of the season after Kidderminster were relegated to the Conference National. He signed a 12-month contract with Scarborough in June 2005, but despite initial optimism, the spell was not successful and with Scarborough in disarray, Simon was in need of a new club for the 2006–07 season. Weaver signed a short-term contract with Conference National side York Cityat the beginning of the 2006–07 season but having been an unused substitute for the first two games of the season, he was released by York so that he could take up the offer of a 12-month contract at Tamworth. Although Weaver played in many of Tamworths games in the 2006–07 season, he was not offered a new contract following the club's relegation. In the summer of 2007, he briefly trialled with Conference Premier newcomers Salisbury City and had discussions with Droylsden. He was injured playing in a pre-season friendly in Scotland: an injury that required the bones in his foot to be pinned. The injury caused him to miss the first four months of the season but, returning to fitness, he signed for Boston United on 11 December 2007. On 29 May 2008, Weaver joined Conference North newcomers King's Lynn, after failing to agree a new deal with Boston. He scored three goals in 22 appearances but left King's Lynn in January after failing to get a regular start in recent weeks. He joined Redditch United, debuting in their 2–1 victory at Hyde United on 31 January 2009. After one further appearance for the club in the away defeat to Fleetwood Town a fortnight later, Weaver rejoined his former club Ilkeston Town. He made a successful debut for the club, netting twice in a 4–3 Northern Premier League Challenge Cup victory at Boston United on 18 February 2009. Weaver was appointed as the new player-manager of Harrogate Town on 20 May 2009. After becoming manager his father Irving became chairman and "the Weavers have transformed Harrogate from sixth-tier strugglers to National League high-flyers challenging for an English Football League place".
