Hi Terry,
I've had plastic (the black cover you mention) and currently have basses with brass and chrome back plates. The brass and chrome look nicer, for some have a better wow factor, and require just a little more care for something most people never see. Yes, the brass will add more weight, but to me it's negligible compared the total weight of the bass it's on. Even so, I still prefer the lighter plastic.
If you have a custom back plate made you should make sure that the person you hire knows the length of the screws and the depth of the recessed threaded posts the screws insert in to ensure the proper fit and thickness of the new plate before anything gets cut.
Hopefully one of the moderators, or others can better address your questions. I can make some guesses, but guesses they would be.
best of luck,
Mike