In his second season with the Rockets, Weber was named to the WHL roster for the 2004 ADT Canada-Russia Challenge in Red Deer and Lethbridge, Alberta. In the two games played, he recorded one assist. At the completion of the regular season, Weber had improved his offensive statistics from the previous season, recording 32 points in 60 games. Weber was named the WHL player of the week for April 6–12, 2004, after recording one goal and six assists in four Kelowna wins over the Tri-City Americans as the Rockets eliminated the Americans four games to two in the Western Conference semi-finals. He finished the WHL playoffs with 17 points in 17 games as the Rockets were eliminated four games to three by the Everett Silvertips in the Western Conference finals. Despite being eliminated from the WHL playoffs, the Rockets advanced to their second consecutive Memorial Cup as the host team. At the 2004 Memorial Cup, Weber was named to the tournament all-star team after recording four points in four games played as the Rockets defeated the Gatineau Olympiques 2–1 in the championship game to win their first Memorial Cup. At the completion of the season, Weber was named to the WHL Western Conference's second all-star team.