A balance weight is secured to a driveshaft tube for rotatably balancing the driveshaft tube during use. The balance weight includes a first inner layer of material and a second outer layer of material that are secured together to form an integral unit. The first and second layers of material may be secured together in any desired manner, such as by adhesives, pressure bonding, tinning, and the like. The inner layer is preferably sufficiently flexible to bend with the driveshaft tube during use and is preferably formed from a material that does not react with either the material used to form the driveshaft tube, the material used to secure the inner layer to the driveshaft tube, or the environment in which the inner layer is used in such a manner as to reduce the ability of the balance weight to be retained on the driveshaft tube. The inner layer can be formed from a stainless steel alloy having a relatively small thickness that allows it to bend with the driveshaft tube during use. The outer layer is preferably formed from a material that also is capable of bending with the driveshaft tube during use, but has high weight density so as to be capable of balancing the driveshaft tube while maintaining a relatively small physical size. The outer layer may be formed from lead or a lead alloy material having a relatively large thickness. One or more grooves may be formed in the outer surface of the outer layer to facilitate flexing of the outer layer with the driveshaft tube. The balance weight is secured to the outer surface of the driveshaft tube by a layer of adhesive that bonds the inner layer of the balance weight to the outer surface of the driveshaft tube.