Goals from Jack Muldoon, Jack Diamond and Lloyd Kerry saw the Sulphurites follow up last weekend's 3-0 home success over Carlisle United with an impressive 3-1 victory against opponents who have already wrapped up promotion to League One.
And Weaver hopes that his injury-ravaged squad, who had lost four on the spin prior to beating the Cumbrians, will take plenty of encouragement from both the result and the nature of their performance.
"We wanted to win the game by passing the ball and I thought we passed it in the second half as well as we have since the Leyton Orient game earlier in the season.
"Once we settled down and worked the ball better, kept the ball better, we prized them open on a number of occasions, not just for the goals.
"I hope it breeds belief into the players, we've got some talented lads. We've had a rocky time in recent months but the injuries with the depth of the squad, there's been a cumulative effect, it's been one after the other and it has been hard.
"It's spiralled with the injuries, it's been like the perfect storm, that and a little bit of lack of confidence, but it's great to see confidence coming back to certain players and us scoring some goals today.
"It's a great win at a very difficult place to come. I think this makes us all feel better and it doesn't take long when you bag wins together for the table to start looking a little bit better and we will aim to win the game next week as well."
Muldoon calmly fired Town ahead from the penalty spot on 40 minutes following Kane Wilson's trip on Diamond inside the Forest Green box.
Rovers were then awarded a controversial spot-kick of their own deep into first-half stoppage-time when Sheron was penalised for what looked like minimal contact on Wilson.
Jamille Matt made no mistake from 12 yards, however the Sulphurites were back ahead within a minute of the second half kicking off as Diamond brought the ball down on the edge of the area and dispatched a fine finish into the bottom corner.
Kerry then wrapped things up on 73 minutes, finishing confidently beyond Luke McGee after Luke Armstrong and Diamond kept a Town attack alive before Muldoon worked the ball into the substitutes' path.
But, as pleased as he was with the way his side passed the ball and took their chances, Weaver was also thrilled by an all-too-rare decent defensive display.
"There were some great blocks and some great displays across the back-line," the Town boss added after watching Warren Burrell and Nathan Sheron prevent certain goals with some excellent work on their own line.
"I thought that all the defenders wanted the ball as well, which is what we want. We don't just want to launch the ball and hit and hope, I thought there was great composure throughout by all of them across the back.
"George Thomson in particular was bringing balls out of the sky and starting play instead of just hooking it away and out. And, Josh Austerfield just sits there in front as a designated holding midfielder, who distributes with great composure.
"Everybody put a shift in, the recovery runs were fast when we needed them, we broke up play and then counter-attacked with ease at times, it was really exciting to watch."
Saturday's victory lifts Town two places in the League Two standings to 17th and takes them on to 53 points for the season.