Midfielder Ellis Taylor is expected to be out for about three months with a thigh strain, while defender Bobby Faulkner is recovering from hamstring surgery.
Forward Conor McAleny has returned to training this week, while long-term midfield absentee George Thomson continues his rehab.
“To see an inspirational player, [Thompson], one of the best players in our history out with the ball, passing, getting his boots on again, really does give us a new buzz,” Weaver said.
“It gives us hope that a return is around the corner. We would hope for some full-on training by the end of December and in the start of the new year. I’d dearly love to get him involved in the selection process.
“[Faulkner] has had his operation, it was successful. He is hoping for [the] end of January [to return]. We’ll have to be led by the experts on that one.”
Under Weaver, Harrogate have finished between 13th and 19th in each of the past five full seasons.
He has been managing the club since 2009, comfortably making him the longest-serving manager in the top four divisions ahead of Manchester City’s Pep Guardiola and Arsenal’s Mikel Arteta, who are the only other two to have joined their clubs before 2020.
