The BAIIIs are not top loading that I see. Also, are the BAIII's direct replacements for the original 5 screw Fender style bridge? I thought the BAIII was only for the new style string-thru-body Fenders.
If you are referring to the 5 screw Smith "IV" Bridge then, yes, it is a direct replacement and has the same footprint and mass as a BAII, but is a much better bridge IMO.
The BAII as I knew was 'cast' Zinc. The Smith Bridges are All 'Machined' from Solid Brass stock.
I think the Brass has a bit more Mass than cast Zinc does. I used BAIIs for our Basses in the first couple of years until we started making our own. The Owner of the company Glenn Quan was a good friend and even sold us un-plated Blanks to engrave our own name in it. Our Bridge is similar in design but with the Quick Release and solid machined brass, I would consider it a step up or so. I still believe the BAII to be a great bridge if that's what you like. Our direction in design took us down a different road as things evolved for us.
Fascinating, thanks for the background Ken! I really like your bridge on my Palaedium. It replaced the original Badass II and it's very easy to see it's a similar design. IMO it's a better piece.
Mass? 
