A weight training exercise apparatus incorporates a handled bag to receive a weight bag containing a mass of granular material having a weight. The weight bag is formed with a sheet of flexible, pliant material, and has a bag chamber formed by and between a closed end and an opposed mouth and opposed closed sides formed by opposed hems formed in the sheet extending between the closed end of the weight bag and the mouth. The hems extend into the bag chamber, which is filled with the mass of granular material. The mouth is formed with primary and second seals to close the mouth to prevent granular material from spilling from the mouth.