Corrected entry: In the film's numerous SCUBA scenes nobody is ever wearing buoyancy compensators. These are inflatable and deflatable vests SCUBA divers use to adjust their buoyancy. Nor does anyone wear any weights. Because of the positive buoyancy of the human body, wetsuits and air canisters none of these people should be able to submerge at all.
Correction: Cylinders are heavy, and short rubber wetsuits produce little buoyancy, so weights are not necessary to sink. Correctly weighted BCDs aren't required either. The equipment shown was typical for the time and, obviously as the scenes are shot underwater, worked perfectly well.
Correction: Since all the underwater scenes were actually filmed underwater, this is obviously untrue. Alternatively, this can be put down to some genius innovation available only to secret service operatives (Like the air canister that's no bigger than a pen which Bond uses).