Originally Posted by mas502arc
Fender Aerodyne Jazz?
I was going to suggest the same thing, once the OP replied to my question. So, I'll assume it's the A-string he wants to drop up-and-down. But, given how much of it fits his criteria, I'll second the motion.
It's much lighter than a regular Jazz bass. A lot of that comes from the carved-top body and possibly the tighter neck radius, but don't quote me on that. But when you're dealing with an ounce here and there, every little bit counts. Mine comes in at almost exactly 8.5 pounds. I've seen some people install Ultralight tuners to drop even more weight.
And speaking of tuners, the Hipshot BT10 is a perfect match for mine. I didn't have to add any new holes onto the back of the headstock. It just dropped right in!
As far as cost goes, they're about $800 brand new, but I've seen plenty go for somewhere around $500 used, even ones with some small mods (tuners, pickups, etc…).
As for the nut, you might need to widen the slots or even install a new one. I've never tried to use anything heavier than a 105 on mine. However, the synthetic bone seems to be pretty sturdy.
On the topic of "what you're playing", it's capable of a nice variety of sounds. It's got a P/J configuration, and when coupled with the right strings, can produce a wide range of tones.
Oh, and I must always mention this, it's sexy as Hell!
Last year, with copper-plated D'Addario Reds…
…and this year, sporting DR Black Beauties.