Dean - if you have the time, try this.
1. Disconnect all control cables and the wiring from around the headstock i.e. instrument panel, left and right switches (you'll need to hang these forward of the forks), throttle, clutch and fast idle. If you can't easily disconnect the control cables, make sure there is as much slack in them as possible where they curve up to the handlebars. Make sure they don't catch anywhere when you move the bars from lock to lock
2. Jack the front of the bike up until the front wheel is just clear of the ground
3. Centre the handlebars
4. Put both hands one on each of the fork bottoms. Gently try to rock the steering assembly from front to rear. You are testing for the slightest amount of play - there should be absolutely none. Don't be fooled by the bike moving, which is why I said 'gently'. Any movement might be removable but... read on
5. Hold one end of the handlebars lightly in your fingertips and move the steering assembly from one side to the other. It should be absolutely smooth. Any feeling of 'tick-tick-tick' resistance coming through the bars is a sign of brinneling in (most likely) the lower headstock bearing outer raceway. 'Brinneling' is where the taper rollers have punched a groove in the outer raceway. This is a replacement job.
6. Make sure the handlebars are still centred. Tap the end of the bar sharply but not hard. The whole steering assembly should fall off to the otherside in one smooth motion. Any sign of resistance, first check that you're not snagging any of the cables. If there's no obvious snag then your headstock bearings are possibly too tight.
7. If you don't find any signs of brinneling, then (4) could be the headstock bearings being slightly too loose
Loose, tight or brinneled headstock bearings will all cause a weave. I don't know about Clymer but Haynes have lifted the BMW description of how to set the headstock taper rollers verbatim from the OEM workshop manual. That description assumes that the outer taper raceways are not fully seated after they have been pushed/pulled in. I always keep at least one outer raceway from every taper roller bearing I have ever changed. I tap the raceway flush with the headstock, then use the old raceway to drive the new one fully home. It goes in approximately a further 2mm from flush. I then adjust the bearings so that the tap test (6) is stiff. From there, I slacken off the adjuster in tiny increments doing the tap test while still testing for looseness (4). When the tap test moves quickly and smoothly but there is no looseness, the bearings are properly adjusted. This assumes that you did seat the outer raceways as described.
There are other methods for setting taper rollers but most of them assume the outer raceway is not fully home and start by getting you to keep tightening up the bearings until the bearing is pulled hard home. I don't like this method because if you're not familiar with the procedure, too much pressure can start brinneling in a brand new bearing.