A low speed "weave" .... hands on the bars, hard to keep the bike tracking straight, goes left than right etc. is caused by too tight, dry, or bad steering head bearings.
A low speed "shimmy" with hands off the bars or held lightly usually while decelerating is caused by too loose or worn out steering bearings.
A high speed "weave" in turns is mostly due to the frame design and swing arm flexing and in my experience is generated in the rear of the bike.
A high speed "weave" when going straight can be a number of things; tires, fairing, seating position, steering head bearings and it's all made possible or worse because of the frame and swing arm deficiencies.
A high speed "wobble", "shimmy" or "tank slapper" is usually caused when the front end gets unsettled at speed after hitting a bump on the road. Less than great forks, frame, tires and too loose steering head bearing are likely causes.
If you like going that fast, then carefully maintaining the suspension, steering and tires is critical. After that, better springs/shocks in the front and rear, solid motor mounts, a fork brace, a braced swing arm will all make incremental improvements. And of course radial tires are a big improvement.
On my last Gen 1 I had a Racetech front suspension, Works shocks in the rear, a fork brace and solid motor mounts. With this combination I never had any sign of a high speed wobble with bias ply tires. You could still feel a weave on really fast sweepers (again coming from the rear) but it was never scary...just a little uncomfortable.
On my Gen 2 I can run to 170 MPH and the bike feels like it is on rails. It has a very stiff frame and swing arm, and the front forks are huge. It really feels like it's all one piece at speed.