The 23-year-old former Republic of Ireland youth international is one of eight members of the Sulphurites’ squad who will leave Wetherby Road this summer upon the expiry of their contracts.
He made 29 appearances in all competitions during 2021/22, a campaign which saw him struggle with injuries and illness, starting just 10 matches.
And, although the ex-Norwich City attacker demonstrated the quality he possesses on plenty of occasions, it is concerns regarding his durability that mean Town have decided against offering him a new deal.
"Simon Power is a player with loads of talent," Weaver told the Harrogate Advertiser.
"He could well end up playing at a higher level in the future, he has certainly got the ability. When he has played this season he has done fine, he's had some really good games
"But, we're in a position where we need to be confident that he will be able to start 30-35 games a season, and the way things have gone this year that doesn't seem like it would be feasible at the moment.
"We took a bit of a chance on him when we brought him in from Norwich and I always think back to the game away at Crawley last season when he tore them apart with his pace.
"He's one who we really hoped would be staying at the club for a lot longer and it's a shame to see him move on, however I know that he is young enough and good enough to go again somewhere else."
Power joined Town from Norwich on a permanent deal in January 2021 following a successful loan spell at National League outfit Kings Lynn.
He went on to make 42 competitive appearances for the Sulphurites, netting three goals in the process.
His last outing in Harrogate colours came in the final-day-of-the-season defeat at home to Sutton United, during which he was introduced as a 65th-minute substitute before being forced off through injury a quarter-of-an-hour later.