The following season Weber began his rookie season with the Rockets. Early into the campaign, Weber established a physical presence, often fighting opposing players. Overall, he had 167 penalty minutes that season, the most in his entire playing career. Offensively, Weber finished his rookie season with eighteen points in seventy games played. He also scored 5 points in 19 playoff games as the Rockets won the franchise's first Ed Chynoweth Cup as WHL champions, defeating the Red Deer Rebels in the finals. As WHL champions, the Rockets represented the WHL at the 2003 Memorial Cup in Quebec City, Quebec, where they were defeated by the Hull Olympiques 2–1 in the semi-final. At the completion of his rookie WHL season, Weber was eligible to be drafted into the National Hockey League (NHL) at the 2003 NHL Entry Draft. Heading into the draft, he was ranked 42nd among North American skaters by the NHL Central Scouting Bureau and 54th overall by International Scouting Services. On June 21, 2003, he was drafted in the second round, 49th overall, by the Nashville Predators.