A pipeline weighting device to straddle the longitudinal axis of a pipeline, a method of filling the device, and a method of weighting a pipeline with the device. The pipeline weighting device is formed of a plurality of interconnected, generally tubular-shaped lobes arranged to straddle the pipeline in a balanced manner along the longitudinal axis of the pipeline. The lobes are formed of a flexible, water permeable fabric to hold weighting fill material. Each lobe has opposed and closed longitudinal side edges and opposed ends, one end being a closed end, and the other end forming an open or partially open filling end. Each lobe is formed with a self-closing filling sleeve or filling flap at the open filling end, the filling sleeve or filling flap extending into the interior of the lobe and providing an opening into the lobe in a manner such that, when each of the lobes is fully charged through the opening with the fill material, and the pipeline weighting device is turned on its longitudinal axis, the filling sleeve or tube becomes trapped to close the filling sleeve or filling flap and to contain the fill material.