With the benefit of the addtional photos in the auction link, I agree with John about the use of cane slices.
The canes are formed as: central core of clear within thin green coating within white coating followed by a fairly thick coating of purple / amethyst. When sliced they will all be a perfect buillseye type cane - amethyst over white over green over clear centre.
At the stage of "picking up the canes" and other shaping (see below) the roundness of the canes will be affected by each cane pressing against the next. In normal cases where the canes are set together as if it were "six-around-one", the "pressing together" will form a hexagonal shape to the "central" cane. When used as a full covering a whole series of "six-around-one" will be apparent and all the canes will show more-or-less straight edges forming lots of hexagons.
But when the canes are not set exactly "side by side" to the same extent, then the forming of a hexagin will take on varying shapes - including no shaping at all thus showing a (mostly) perfect circle. These varied effects can be seen clearly in the auction link example.
I suggest (in principle) the basic working to be ...
a) gather(s) of clear glass as needed to make a required internal size
b) add the "fancy bits and pieces" (air bubbles / flecks)
c) add a thick-ish coating of clear to get to a required size
d) roll onto marver to pick up the cane slices
e) shape to the basic domed form
f) final gather of clear and final shaping
I do not understand what the internal "fancy bits and pieces" really are, nor at which stage they would be added to the construction of the weight, so my stage b) is certainly open to question.
I did wonder if the "fancy bits and peices" were part of the central core of the cane but that seems too complex. Much simpler is addition of "bubbles / flecks" to the central mass of the weight at the proper stage. This would allow the clear centre of the cane to give the view into the depth of the weight.