The Rays designated Weber for assignment Saturday, Marc Topkin of the Tampa Bay Times reports.
Weber churned out a 2.05 ERA in 74.2 innings for Triple-A Durham this year but was saddled with a 5.06 ERA in 5.1 big-league frames. The 27-year-old will either accept a minor-league assignment with Durham or get a chance to find a depth role with another organization via trade or free agency.