A trike won't weigh much more than a bike actually. Unless you do something hideous like a local just built around here. His has diamond tread toolboxes and a gun rack.
The motor in your '80 makes more power down low than the SOHC bikes did, I think it'd be an awesome engine for a trike. Relatively light, air cooled for simplicity, reliable and plenty of power. I'd be very interested in watching this come together once you start building it!
I was tossing around the idea of a trike a while back but never got off my bum. While considering rearend options I thought something out of a small car would work well and be inexpensive to find. Maybe a rear diff out of a Subaru? I know some of the earlier ones ('70's) are pretty compact and shouldn't rob much power.
Four wheelers is another vehicle that you could source a light weight differential out of, but they might be too narrow. Personally, I think they might not be stable enough for highway speeds.
Cycle-X's rear diff is an awesome piece if you don't mind spending that much. Servicar rearends aren't the easiest things to find, at least around me. I've tried.
There are companies like Moser Engineering that will build you custom axles (the inner part, not the housing) for a few hundred dollars. I don't know what your skill level/tool availability situation is, but maybe cut down a rear end to the width you want?
Toyota pick up rear diffs are super light and have a nice clean look to them. Not gaudy at all. You could probably get on out of a junk yard for $75-100 complete with brakes. Cut the axle tubes down to the width you want and then get Moser, or a similar company, to either make you a new set of axle or even just shorten and respline the existing axles. Shortening and resplining is usually frowned upon, but in this situation it'd be plenty strong enough. That gets you going for ~$400 vs $1,400 for a Cycle-X rearend.
The problem with using some sort of auto diff as getting it connected to a chain driven cycle engine. It would require some sort of gearbox and that would end up just eating power to operate. That's why my brain kept thinking about ATV rearends. Most chain driven ATV axles don't have differentials,though. Servicar rear axles are the only "readily available'' things that are chain driven and have a diff in them.
There's got to be a cheaper, easier to find option than Servicars and Cycle-x. I think I'll go on the hunt for this again...