Weaver, 21, was a three-year starter at Boise State. He was selected with the No. 164 overall pick in the fifth round by the Dolphins.
Weaver signed a four-year, $3,602,992 contract with the Dolphins that includes a $307,992 signing bonus. Miami waived Weaver with an injury designation on Monday.
During his college career at Boise State, Weaver recorded 128 tackles, 47.5 tackles for a loss, 34 sacks, two interceptions, three forced fumbles, a recovery, a defensive touchdown and six passes defended over the course of three seasons and 40 games.