On September 10, 2004, Weber signed a three-year, $1.425 million entry-level contract with the Nashville Predators. A year-and-a-half later, Weber made his NHL debut on January 6, 2006, against the Detroit Red Wings, recording three shots on goal in 11:08 minutes of icetime. Three months later, on April 6, 2006, he scored his first NHL goal, against Reinhard Divis of the St. Louis Blues in a 3–0 Nashville victory. Weber went on to play in 28 games during his rookie season, finishing with two goals and ten assists. He also scored two goals in four Stanley Cup playoff games with the Predators before the team was eliminated in the first round by the San Jose Sharks. With Nashville's American Hockey League (AHL) affiliate, the Milwaukee Admirals, still in playoff action, Weber was reassigned to the Admirals' roster for the remainder of the AHL playoffs. He recorded 6 goals and 5 assists in 14 games during his time with the Admirals, who finished in second place in the Calder Cup, losing to the Hershey Bears in six games in the Calder Cup Finals.