Not sure what that is! Do you mean the whole bike is weaving or are the forks misbehaving!Has it suddenly happened ? Just a thought, but are your wheels tracking properly and check that they  are they both vertical, but the latter would suggest a bent frame!Other than your alcoholic content, I'm at a loss!!

I had a '72 Yamaha that had a persistant "head weave" as you put it (a slow head shake) at certain speeds. I, too, did all the usual allignment, tires, shocks, fork oil, etc. I finally gave up on it and traded for a '77 Kawasaki KZ-650 (my sollution).  Looking back I think it most probably was a built in defect in the frame,chassis,design but I had that thing for several years and over 40,000 miles and never fixed it.
I am surprised that a 90's anything should suffer from such basic handling deficiencies.

Rod

I'd try a new, different front tire first.

I assume you've checked all the basics like tyre inflation pressures and preload on the head bearings. This could also be down to swingarm pivot bearings.
Without a more precise description of the problem - speed range it happens in, on the brakes, on the gas, over white lines etc it's very hard to diagnose any handling faults.
I suspect that if everthing else on the bike is eliminated as a cause then you could have frame damage you don't know about.

I have heard of wing mirrors causing weaves - might be worth a try.

Sounds like a "tank-slapper". Does your bike have a fork brace? If not, I've heard that helps on some bikes.

Otherwise, the cause may be due to the type of tyre, or alignment, or head bearing adjustment, or ...

You might like to check the swing arm bearings, for movement. A common cause.

Harvey.