Town produced two controlled displays to see off neighbours York City 2-0 on Saturday before repeating the performance to assert their class on Tadcaster Albion 3-1 on Tuesday evening.
Returning forward Dominic Knowles fired Town ahead inside four minutes against York with a cool finish in front of the home faithful.
Peter Crook kept Town ahead with a fine save shortly before half-time, and the win was sealed when midfielder Lloyd Kerry’s shot from distance crept past the York keeper in the 87th minute.
Weaver said: “It was a really good confidence booster. No one is getting carried away because it’s only pre-season.
“I couldn’t fault the sticking to the game plan and staying as a unit but looking a threat. We look like we can score goals.”
Promotion-hunting Tadcaster were expected to provide a stern test for Town at the i2i Stadium under ex-Harrogate Railway manager Billy Miller.
The two sides matched each other in a tight first half, with Louie Swain fashioning the best opportunity only to see his goalbound clip over keeper Gary Stevens cleared off the line by George Bissett.
The game turned on its head, though, as Tadcaster – who were undone by a late show at Scarborough Athletic 3-0 on Saturday - capitulated within 10 minutes of the second half.
Town winger Jordan Thewlis drilled home from 20 yards to make the breakthrough before the same player had an opportunity to double the lead a minute later from the penalty spot.
After being hauled down by Danny Stimpson in the box, Thewlis saw his spot-kick saved by keeper Gary Stevens low to his left. Stevens was put to the test from 12 yards just two minutes later, as Town were awarded a second penalty. However, triallist Connor Bower blazed high and wide.
The second goal came courtesy of a Stevens error as he cleared straight to another triallist, Royal Johnson who pulled back for Swain to crash home.
Town stretched their legs again on 75 minutes as the impressive Bower – who has been offered non-contract terms at the club – stole a yard in the box and swept into the bottom corner.
Albion regained their focus with the first appearance of former Town defender Matt Heath in a yellow and blue shirt. And Josh Barrett gave Miller’s something to cheer in the last five minutes as he slid under replacement keeper Dan Atkinson.
Weaver said: “I have enjoyed this pre-season with what’s happened on and off the pitch for me.
“We have a dream to do well at this club. I certainly have and the directors share it.
“We have to be really resilient, even if we have a spate of injuries, we have to keep going. As long as you can see us doing it, and I can, then I will crack on.
“I think this is the freshest, most hungry group we have had. But it’s also the most down to earth group as well. We haven’t got anyone standing out and being arrogant.
“They just want to turn up and do well. They’re mixing well, so it’s so far so good.”