I've posted it elsewhere but here it is...again.
You have to pre-load the stem, that is, the distance between the major diameter of the threads on the stem is a known distance so when you pre-load the stem using the OEM tightening sequence, you remove all the freeplay and set the bearings at basically '0' clearance.
As follows...
Section 14.15 inclusive...
You have to remove the handlebars and instruments, I won't cover that, just the adjustment.
Slacken and remove the top nut and washer. Lift and remove the handlebar and top yoke assembly to gain access to the bearing adjuster nut and locknut....It is assumed that you have already removed the fork tubes. If not, leave the tubes clamped in the lower yoke and remove the top yoke.
-Slacken the adjuster nut
-Adjust the bearing freeplay as follows....
-Tighten the adjuster nut to 40Nm.
-Slacken the adjuster nut fully.
-Re-tighten the adjuster nut to 6Nm.
-Loosen the adjuster nut by 90 degrees (no more, no less 90 degrees is the extrapolated distance of freeplay in the threads)
-Hold the adjuster nut in that position while tightening the locknut to 40Nm (ensure that the adjuster nut does not move while tightening the locknut).
What you have done is pre-loaded the stem bearings by removing the pre-determined freeplay in the threads themselves. The stem bearings will, at that point, be at a zero freeplay state.
I would also suggest before making the adjustment that you completely remove the stem, clean out the old grease and repack the headstock cavity with fresh, high quality, synthetic grease and re-pack both the upper bearing and lower bearing with a pressure bearing packer using the same grease. To do that, the fork tube have to be removed from both the upper and lower yokes, that will entaqil removeing the front wheel, fender, brake caliper and assorted parts. Upon reassembly, pay close attention to proper torque values and tightening sequences. The reason is simply that the factory grease gets contaminated by moisture due to washing the bike and road spray. The seals aren't moisture proof, just resistant. If you are really industrious, while the stem is completely out, drill and tap the headstock in 2 places (near the top and bottom but not in the outer race areas) for alemite fittings. Then you can give the headstock bearings a shot of grease ocassionally to keep the headstock full of uncontaminated grease and prolong the life of the bearings.
Most OEM manufacturers on the assembly line, apply only a minimum amount of grease which leaves the cavity prone to moisture ingress and eventual rusting and destruction of the bearings themselves.
With the front end elevated off the ground, the entire assembly (forks, wheel handlebars, everything) should articulate from lock-to-lock without any binding or roughness. There should be no hesitation whatsoever but, at the same time, it should not just flop from side to side which is a good indicator of excessive freeplay.
Triumph gives no starting torque figure in the shop manual. Usually, a starting torque value is given for preload, that is, how many Nm's or Lbft it takes to start the assembly in motion.
While moving the bars lock to lock, it will be quite easy to feel and ascertain whether there is too much or too little freplay and p-reload. It should be a smooth movement with no hesitation. A flopping side to side movement is very indicative of too much freeplay as is wobbling on the road. If the assembly is too tight, the bike will exhibit a self centering condition and it will resist you in cornering. Also, a too tight preload will quickly wear the bearings and cause the races to flat spot which you will experience as reough steering.
Bar weights have no effect whatsoever on headshake. The function of bar end weights is to cancel any harmonic vibration induced by the engine. Removing the weights and filling the bars with steel shot will have the same effect.
The headshake is entirely dependent on bearing preload and to a lesser extent on the trail of the front wheel. The trail is determined by axle placement and the angle at which the upper and lower yoke are bored at in relationship to the angle of the headstock itself. Those dimensions are determined by the OEM and are not easily changed.