[Arran]

I believe that the 40-216RX has two power transformers, one for the radio receiver portion of the chassis, and another for the remote control receiver and stepper unit. Part of what would make the speaker lighter is the fact that the output transformer is mounted on the radio chassis and not the speaker basket, but the rear bracket holding the field coil is also not as heavy gauge and has no mounting ears like the speaker of a 37-116 would have. The 40-216RX also does not have any acoustical resonators to add to the weight, but this is likely offset by the extra parts involved in the remote control mechanism. The weight of the remote control box is pretty negligible, without the battery pack inside it may weigh a few pounds. I would not personally go to the trouble and expense of having any of the '16 series mystery control sets shipped, they seem to be common enough that a more local example will turn up at some point, not to mention the rubber/gutta percha wiring you often have to deal with to restore one, even in the remote control box.
Regards
Arran