For the 2013–14 season, Weber led all NHL defencemen with 23 goals, which also matched his career high. He broke Kimmo Timonen's Predator record for single-season points by a defenceman with 56 points, which also led the Predators for the season. On April 28, Weber was named a finalist for the Norris Trophy for the third time in his career; the other finalists were Zdeno Chára and Duncan Keith, the latter of which won the award. Weber finishing third in voting.