The fixture, originally due to be played on Saturday but then postponed due a waterlogged pitch, was hastily re-arranged by the Bees despite a bleak weather forecast.
And, when the heavens opened almost immediately upon kick-off, the already-saturated playing surface at The Hive quickly began to deteriorate.
The first half of the game was completed, however with the scores locked at 1-1, referee Gary Parsons deemed the pitch to have become unplayable and called a halt to proceedings during the interval.
A frustrated Weaver accepted that the decision to abandon the contest was the correct one, but insisted that the match should never have been re-arranged for Tuesday evening.
“I think logic has to play a part sometimes,” he said.
“People want games on, and we all wanted to play tonight, but looking at the Met Office, they don’t often get it wrong. The forecasts these days are very accurate, there was a strong chance of rain from 7pm and the pitch just wasn’t going to hold that rain.
“If it’s not going to hold light rain, then the game should never have gone ahead.
“It’s a fair judgement at half-time to call it off because if the ball can’t bounce or roll then it’s not a proper football game.
“It’s just frustrating, frustrating for fans who’ve taken half a day off work, and we have to come down here again now. It’s the expense of it all and we won’t be recompensed.
Weaver admitted pre-match that he was surprised that the fixture had been re-scheduled for Tuesday, particularly with the weather forecast suggesting that there was more rain on its way.
“I thought it was daft to be honest but they [Barnet] said there was a strong chance of the game being on because they had people on the pitch with forks and wind-blowers, but they needed more than that, let’s be honest,” Weaver added.
“They needed to get lucky for the game to be played and they didn’t. Now it’s wrecked their pitch and we’ll have to come down and do it all again.”
George Thomson’s goal inside the first minute handed Town a very early lead, while the visitors also had two strong penalty appeals turned down before Paul McCallum restored parity seven minutes before the break.