Weber spent one season in Switzerland's National League B, then moved to Canada in 2006 to develop his game. The defenseman had immediate success with Kitchener of the Ontario Hockey League, scoring 96 points in 110 games from 2006-08, and was named to the OHL Second All-Star Team in 2008. He also led Kitchener to the Memorial Cup final.

Selected by the Montreal Canadiens in the third round (No. 73) of the 2007 NHL Draft, Weber spent the 2008-09 season in the American Hockey League and had 44 points (16 goals, 28 assists) in 68 games. He made his NHL debut that season and had one assist in three games. His first NHL goal came in the Stanley Cup Playoffs against the Boston Bruins on April 20, 2009.

Weber spent most of the 2009-10 season with Hamilton of the AHL; he had no points in five games with Montreal. His first NHL regular-season goal came on Feb. 9, 2011, also against the Bruins.

Weber signed the first of three straight one-year contracts with the Vancouver Canucks on July 1, 2013, and had an NHL career-high 11 goals and 21 points in 2014-15. He played 45 games with the Canucks in 2015-16 and had seven assists.

He signed a one-year contract with the Nashville Predators on July 1, 2016. Weber had eight points (one goal, seven assists) in 73 regular-season games. He had one assist in 22 playoff games but helped Nashville advance to the Stanley Cup Final for the first time since entering the NHL in 1998 before losing to the Pittsburgh Penguins in six games.

Weber had five points (two goals, three assists) in 47 games in 2017-18, and scored one goal in four playoff games.

NOTES & TRANSACTIONS

• OHL Second All-Star Team (2008)
• AHL All-Rookie Team (2009)
• Signed as a free agent by Geneve (Swiss), September 18, 2012.
• Signed as a free agent by Vancouver, July 5, 2013.
• Signed as a free agent by Nashville, July 1, 2016.
• Signed as a free agent by Pittsburgh, January 27, 2021.