The Sulphurites went a goal down in the 62nd minute of Saturday’s League Two clash at the JobServe Community Stadium, but Matty Daly levelled matters with a neat finish just three minutes later.
Substitute Sam Folarin, who created Town’s equaliser, then produced a moment of brilliance to win the game late on, turning with his back to goal on the edge of the Colchester box and whipping a fine effort into the top corner.
And it was the away side’s immediate response to that initial setback which left Weaver most satisfied.
"I'm really proud, especially with the reaction to going to a goal down,” he said.
"We've got a determination this year to be the best in the league at reacting to a disappointment. We saw a really positive reaction from the lads and showed a real togetherness and turned it around, turned the game on its head.
"We were on the front foot after going behind, it put some fire in the bellies. Nobody's shoulders sloped on the way back to the kick-off. I could see the lads were lined up and I know Colchester were celebrating in the corner but the lads were like, ‘come on.’
"So that showed a belief and a determination to put things right because you can feel sorry for yourself, can't you? And suddenly there's a hangover effect and the game drifts away, but we didn't allow that to happen today. So that's the most pleasing aspect.”
Town were indebted to goalkeeper Mark Oxley for a fine double save from Chay Cooper in the first half which ensured that they headed into the interval on level terms.
And Oxley was at it again shortly after the resumption, reacting well to keep out Bradley Ihionvien’s powerful header from a Noah Chilvers cross.
The visiting custodian was however powerless to prevent Colchester from breaking the deadlock on 62 minutes. Almost Folarin’s first contribution after arriving on the pitch was to pass the ball straight to Cameron McGeehan, who teed up Cooper to cut in off the left wing and lashed home a superb 20-yard effort with his right foot.
The Sulphurites wasted little time getting themselves back on terms. Levi Sutton swept a pass out to the Harrogate left where a mistake by the sliding Will Greenidge afforded Folarin the opportunity to run at the home defence.
He then slipped a clever pass in behind Zach Mitchell, which Daly ran on to before firing a clinical finish across Owen Goodman and inside the far post.
The U’s came close to reclaiming the lead on 78 minutes, McGeehan curling a long-range effort against the Town cross-bar, but two minutes later, Weaver’s men were ahead.
A Sutton shot was blocked by a Colchester defender, and the ball then broke for Folarin on the left-hand side of the penalty area. From there, he moved back inside with his back to goal before spinning and cracking the sweetest of strikes beyond the despairing dive of Goodman.
With the regulation 90 minutes up, Town had to negotiate a further seven, and they needed another big save from Oxley at the death to prevent Joe Taylor making it 2-2.
Saturday’s win at the JobServe Community Stadium was Harrogate’s first in four attempts, having lost on each of their three previous visits.
On coming away with a positive result at long last, Weaver added: “It feels good, finally winning a game at Colchester.
“We've been here the previous three years and lost games and when we played average, played well, played poorly and come away with nothing.
"It’s certainly a long journey down here and there’s a buzz about the changing room after this. It was a hard-fought win, but I thought that we deserved it.”
Saturday’s victory lifts Town to 14th in the League Two standings where they now sit nine points clear of the relegation zone and just four shy of the play-offs.