The Sulphurites ran out comfortable 3-0 victors in Saturday's 2022/23 curtain-raiser, producing an impressive all-round display at a wet Wetherby Road.
Alex Pattison, Matty Daly and substitute Jack Muldoon all found the back of the Robins' net as a starting XI featuring no fewer than six new signings served up a passable impression of a side that had actually played together before.
"We couldn't really have made much of a better start to the season," Weaver told the Harrogate Advertiser.
"I thought we were good value for the result. I thought that we thoroughly deserved it and we had a penalty shout as well.
"Yes, they had a penalty saved by our goalkeeper, but Swindon are a team of real quality. They rinsed us here last season and we've had to learn lessons about the top of the tree at this level.
"But, you've got to get the balance right because it is one win isn't it, it's only three points and there will be a lot of ups and downs during the season, I'm sure. So, we won't get ahead of ourselves.
"But, in terms of if you could write a script for an opening-day win against a big club like that, they don't come much better and I'm delighted because the lads have walked their socks off during pre-season."
Town are among the bookmakers' favourites for relegation from League Two this term, while Swindon are fancied for promotion, but although Weaver said he was expecting a tough game, he insists that he went into Saturday's contest confident about his team's chances.
"I believed we could win the game. I believe in the lads. I don't think you can go into any game not believing in your team, especially when you work closely with them," he added.
"We thought that there were areas that we could exploit and that we could hurt them if we remained solid. The lads have performed very well in all of their roles today.
"The new lads are gelling with the existing players and they've made good progress through pre-season.
"When you've got someone like Joe Mattock, an experienced performer who has been promoted twice out of League One in the last three years, saying that this one has been right up there with the hardest pre-seasons he's ever had physically, we had confidence that the lads would be fit and last the distance of the game in energetic fashion.
"But, if I'm being totally honest, you're never really sure until the first ball is kicked in anger. I'm not going to lie, with so many changes to the line-up, there were some butterflies in my stomach as we went down the tunnel. But, I'm delighted that they proved that they were ready and could rise to the occasion."
Saturday's success means that Town finish the opening weekend second in the League Two standings.