The Sulphurites came out on top in just two of their opening seven league fixtures, but appear to have turned something of a corner having taken seven points from the last nine on offer.
That mini-unbeaten run has seen them pull seven points clear of the bottom two, and although encouraged, Harrogate's manager isn't getting too carried away.
"It's a start, but I wouldn't say we've got momentum yet, we've got to earn that right," Weaver said.
"With five games in October, there's an opportunity to build on momentum and the feel-good factor off the back of a win, particularly a gritty away performance.
"So Tuesday is a huge game in terms of building proper momentum. We want to go into Saturday's fixture with three wins back-to-back under our belt."
Winger Abraham Odoh and midfielder Levi Sutton face late fitness tests, however striker Luke Armstrong has returned to training after illness and will be available to face the Dons.