Weaver played minor hockey in his hometown the local Brampton Maroons in his early years before joining the Richmond Hill-Vaughan Kings of OMHA. After being a 7th round draft choice of the OHL's Guelph Storm in 1995, Weaver decided to remain playing OHA Junior A hockey to maintain his NCAA scholarship eligibility. The diminutive defenceman acquired a scholarship with the Michigan State Spartans and spent four very productive years in the CCHA that included two First All-Star team nods and two Best Defensive Defenceman awards. In the proceeding off season, he was signed by the St. Louis Blues.