Weaver started as a professional with Sheffield Wednesday before embarking on a 14-year career.
Wednesday currently sit 10th in the Championship, four points adrift of the playoffs, but have been on a run of four defeats in their last five matches.
“I would like to think that Sheffield Wednesday are getting closer to promotion," Weaver told Tribal Football.
“Obviously they have a fighting chance of being in the playoffs but they need to go on a run. They had a great win against Leeds United and I think it was a great move getting a young English manager like Garry Monk."
Weaver's Harrogate are currently second in the National League table in just their second season since promotion.
The former Lincoln City man joined the club in 2009 and his work has allowed the club to go full time.
“I didn't like watching Sheffield Wednesday when they were dropping off and not competing," Weaver added.
“Dropping off and defending deep isn't the Sheffield Wednesday way. It's the climate up here to run around and show energy and press and be intense, and that's the style of football that Sheffield Wednesday need to play."
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