A Mark Beck double against his old side ensured it was the National League North team who made the next stage of the competition, writes Tom Feaheny.
"We have put in a very good performance, every player had a good game, I'm delighted," Weaver told BBC Radio York.
"We knew this was a good test for us against a high level team, we are aiming to play against teams like these very soon, we had to put in a good display for the whole game and this sets a benchmark for us."
Beck who recently arrived from Darlington and certainly made an impact for his new side.
"Mark has taken his goals well and really impressed me, this really pleased me and he deserved to be on the scoresheet."
Weaver now has his eyes firmly focused on the upcoming league games.
"There are a lot of games to go, this team has the talent to score the goals and get clean sheets, we are enjoying it and look forward to the games coming up."
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