Abstract: An apparatus for stabilizing an underwater object such as a pipeline includes at least one pair of weights supported on a blanket with the blanket adapted to be disposed across and in engaging contact with the top of the underwater object so that the weights are disposed on opposite sides of the object and a flexible connector between the two weights so as to allow the weights to apply compressive forces to opposite sides of the underwater object to assist in retaining the weights in position relative to the object. A method is also disclosed for laying the underwater object by clampingly placing the afore-described apparatus on the pipeline as it is lowered into the water.