Being an engineer, I am intrigued at all of the responses regarding the causes for front end 'wobble' or 'shimmy'. Having wrenched on many vehicles and bikes over the years, I feel that I have a unique perspective on the causes of this phenomenon.
In this case, I am convinced the wobble/shimmy problem is due to any one of the following (in order of likelyhood):
1) Front tire out of balance or wheel out of round - Can be caused by sitting for a long time, low air pressure, hitting an object hard, bad bearings, tire defect (internal delam), or worn out tire. A problem with the rear tire could also cause a similar issue. Don't assume that the tire is balanced unless you actually check it again at the time you are performing your analysis. As it is spinning, check for a hop or distortion in the tire or wheel. Heavy, rotating assemblies are notorious for creating harmonic type vibrations or movements. If your wobble goes away at a certain speed, you have certainly identified a rotating assembly balance problem - no question.
2) Steering Damper - Worn out seals or no fluid inside damper. This damper is designed to dampen lateral road input and/or rapid user input to the pivot of the steering forks. If not enough resistance is offered during a frequency input, it will allow a harmonic 'shimmy' to develop. One way to test the damper is to raise the front wheel off the ground and rapidly cycle the handlebard right to left. If you feel a significant resistance doing this fast versus slow, then the damper is probably working. If you see evidence of a leak around the piston rods, you should replace the damper.
3) Front Shock - Worn out, no damping effect. If the roadwheel is not kept from bouncing on the pavement, this 'hopping' may feel like a wobble or cause a shimmy. Leaking shocks are a giveaway, but are not the only way to tell. If you drive slowly along and stop suddenly using only your rear brake, it will cause the front end to dive. The bike should only bounce 1X (down-up-stop). If it goes for more than that, the front shock should probably be replaced.
4) Front Telelever - Worn or loose ball joint or other main suspension component. Same as #3
If all of these areas/components truly check out ok, there is a likelyhood that there may be a problem with your rear suspension or frame alignment.
Balancing tires requires a good, repeatable technique. In the case of a shimmy being solved by balancing of a front tire, and then its return 3K miles later, I would remove and rebalance the tire/wheel again. Spin the tire multiple times to validate the balancing before mounting it back in the forks. Tire characteristics change over time and may cause out of balance condition. Riding style and road conditions play a big part of why this happens. Sometimes a balance weight is thrown off and there is no evidence that you may notice (i.e. no adhesive residue). You might think that the weights that are there are the weights that were applied at the last balancing. Sometimes the tire is just defective due to belting defects or compound thickness uniformity issues.
I hope this helps shed light on these hard to diagnose issues.