The leash assembly includes a leash mechanism with a body, a cord, a clip and a handle that extends from the body. The body presents two spaced apart circular sides with outer peripheral edges. The cord extends from an interior of the body between the circular sides to a free end. The clip is attached with the free end of the cord for attaching the cord with the collar of the animal. The leash assembly further includes a cover with first and second portions which at least partially cover the circular sides of the body of the leash mechanism. The first and second portions of the cover has outer peripheries which generally follow at least a portion of each of the outer peripheral edges of the generally circular sides of the body. The cover contains a high density material for increasing a mass of the leash assembly.