The Bluebirds were promoted from the National League alongside Harrogate in 2019/20 but found life in League Two far more of a struggle.
While Town briefly flirted with the play-offs and never looked in any serious danger of being sucked into a relegation battle during their debut Football League campaign, Barrow did not adapt quite as well.
They became embroiled in a survival scrap and finished 2020/21 in 21st position, just five points above the drop zone.
But under new manager Mark Cooper, the Cumbrians have strengthened significantly and made a bright start to the season, winning two and drawing one of their opening four competitive outings.
“I totally agree that Barrow are stronger now than they were when we last played them,” said Weaver, who masterminded 1-0 home and away victories over the Bluebirds last season.
“I went over on Tuesday night to watch them against Exeter and I was impressed. It finished a draw but Barrow probably did enough to have won it.
“They’ve got more power and aggression about them. They’re aggressive in both boxes, a threat at set-pieces, but they can still play football as well.
“Mark Cooper is someone who I know well. He’s a very experienced manager at this level and understands exactly what it takes to put together a good League Two team.
“Saturday will be a really tough one, but there’s a big appetite for the game among our lads and we’ll be really up for it.” This weekend’s fixture sees Town return to action following a fortnight of inactivity due to a Covid-19 outbreak at Wetherby Road. Five members of Weaver’s squad contracted the virus, but the Harrogate chief has confirmed that he expects at least one or two of that number to feature against Barrow, possibly even from the start.