i haven't come to many final decisions about anything yet. Hashing out the pawn design, but the other pieces will be more difficult because the pip on the top of the queen isn't something that can be turned between centers. I lack most of the skills that go beyond just turning between centers and don't want to get too far into buying chucks, etc (I have a couple of decent chinese chucks that would be fine for this if I make the effort to turn a mandrel base and drill it properly on the lathe - that's hypothetical at this point)
I'm not a good carver, either, so the knight will be a good learning experience. We'll see.
As far as the weights go, I've done so much oddball stuff with small tools in hand that I'm just going to drill them freehand after turning.
William mentioned using a mandrel (something i haven't made yet) and in that case, there's already something to insert a weight into. Felt on the bottoms will cover up the evidence.