Diaz, 28, had 11 assists and was third on the team with 100 blocked shots while averaging 18:53 of ice time in 46 games, but had been a healthy scratch for seven straight games. He will play for Switzerland at the 2014 Sochi Olympics.
An undrafted free agent who signed with the Canadiens in September 2012, Diaz had four goals and 41 points in 128 NHL games. He is in the final season of a two-year, $2.45 million contract and is scheduled to become an unrestricted free agent in July.
Weise, 25, has three goals and nine assists averaging 7:45 of ice time in 44 games.
Selected by the New York Rangers in the fourth round (No. 111), of the 2008 NHL Draft, the 6-foot-2, 210-pound wing has 10 goals and 26 points in 162 games with the Rangers and Canucks. He can become a restricted free agent after the season.
"A young veteran with 162 games of experience at the NHL level, Dale Weise is a winger with a physical style of play who brings additional toughness and grit to our group of forwards," Canadiens general manager Marc Bergevin said in a release.