After his career as a professional footballer with Wrexham was cut short through injury, Steve Weaver spent 20 years coaching and managing the club's centre of excellence, becoming Head of Youth and then Assistant Manager to Brian Carey. Whilst at Wrexha, he first worked with Stuart Webber whom he followed to Wolves in 2008 and Huddersfield in 2016. Before joining Wolves, he had a brief spell at Manchester City. His six years at Molineux included a spell as first-team coach under Terry Connor when Wolves were in the Premier League.

He spent six years with Wolves and then scouted for Ipswich before joining Webber at Huddersfield in May 2016.

He followed Webber to Norwich in September 2016 and replaced Richard Money as Head of the Academy.

In July 2020 he was promoted to the post of Head of Football Development and will also take responsibilty for all academy football development across the club and also take charge of City’s Under-18 squad. Under new manager Dean Smith, Weaver's role was extended to act as a conduit between the first-team and the development squad, playing a key role in the progression of academy players through to Smith's first-team squad. 

When Dean Smith was sacked by Norwich on 27th December 2022, Weaver and Allan Russell were put in temporary charge of the first team for the games against Reading and Watford.

On 17th April 2024 it was announced that Weaver would be leaving Norwich at the end of the 2023/24 season. 24 Academy players had gone on to play for the first team during Weaver’s time at the club, including Jonathan Rowe, Adam Idah, Andrew Omobamidele and Max Aarons. He said “From when I first joined the football club, the objective was to help improve that pathway and progression of our younger players through the Academy. Reflecting on that now, I think we can be incredibly proud of the work across the Academy. I’d like to thank the Board, players and staff for all of their work and support during my seven years with the club. I’d also like to thank Stuart and Zoe, who could not have given me any more support and autonomy in delivering and running the Academy. I now feel like the time is right for a fresh and new challenge. I’m incredibly proud of everything that we’ve achieved and I’m excited for what comes next.” Executive Director Zoe Webber said: “On behalf of everyone at Norwich City, I’d like to thank Steve for all of his hard work during his time with the club. We’re incredibly proud of our Academy. Steve’s commitment and vision for what he set out to achieve has been integral to our many success stories. He has helped transform our academy infrastructure and facilities, which will stand us in good stead for many years to come.