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.