The STA's (Single Tank Adaptor) that is used for those folks who have a BP/W can have weights attached to the Adaptor. The adaptor is a "U" channel aluminium piece that usually has the weight bar (flat) secured inside using the attach points for the Back Plate.
The "V" weights are placed on the tank bands (of doubles), through the bolts that attach the PB to the doubles rig. The "V" weights are of different weights. The correct weight used is determined by the weight required to become neutrally buoyant at the surface with less than 500 psi. (34.5 bar.) in your tanks. That way should you have to swim to the surface, the diver can still do this with relative ease.
What is my view of "V" weights? I use them when my I use double AL. 80's with my drysuit. They are a nice innovation to this sport.