Lowering the rear or raising the front will sometimes slow or stop a wobble but I'd un tweek the forks first.

 

Yes, it only happens at high speed (around 60 mph and up), and it basically only happens with some sort of external input (eg, a nudge on the handlebar, a wind blast from a passing semi, etc...)
So are you talking the front fork compression damping might need a little stiffening?

 

Mine does it too at speeds above 60. Loosening the grip helps, adjusting seating position helps. At these speeds, the little 300 lb machine has a screaming engine offering some goofy centrifugal stability (or not) and the rider is generally a little nervous. It's not a good freeway bike, even if you have no problem holding the speed.

 

after getting the suspension set for my weight, the klx has been stable at any speed...keep loose...

 

My bike is dialed in close but on loose gravel at speed the bike is down right unstable. Enough so that it is the limiting factor on speed. No woobles but a twichy feeling.

 

Wheel caster or rake is what determines how twitchey the front end is. Straight up and down would have you all over the place. The more you lay the forks back the more stable the front end becomes. You reach a point where excessive rake will cause the wheel to flop over when turned. It doesn't take much to impact steering. This could be the cause if you've messed with the geometry at all.

 

Again, thanks for the feedback.
I went over the front end looking for anything that might be loose, worn, or misaligned, but the only thing I found not right was it had low pressure in the tire. I topped up the pressure and took it for a quick ride hoping that was the problem, but it was still there.
As I've said, it I didn't have the 2009 bike to compare it to I probably would just accepted that the wobble was just a quirk inherent to the KLXs's being and a compromise of design with this dual sport bike, but because it is so much more pronounced on my Son's 2007 bike than it is on my 2009 I feel compelled to see if I can't find the exact reason for it and see if there isn't some way to rectify it.
We just took another 100 km ride yesterday and I didn't see him wobble once, mind you much of the ride was on a dirt mountain road, and I told him we'd switch bikes if he did too much wobbling on the highway, which I don't think he really wanted to do since he's grown very fond of his own bike, and I think that may have been a motivating factor for him to consciously control the wobble.
Anyway, we had a great ride, it was a fine spring day and the dirt mountain road we went over was just dry enough for a couple new and rusty riders to pass and have fun. The snow off the main road was still 2 feet deep, which limited the group of pure dirt bikers we met to the main road as well.
Though I did feel sort of sorry for those dirt bikers being limited to the one stretch of dirt road over the mountain, because after coming down off the mountain, on the route back home, we had a blast cruising a long stretch of beautiful winding country road where they couldn't have legally followed.

 

We haven't messed with anything,,,yet. Although the previous owners may have. I do know the 2007 is a slightly taller bike, and I just measured the two and from back axle to front, and the 2009 is slightly longer. So the 2009 is shorter and longer, perhaps this is indicative of more positive castor in the bike???
Also I noticed the front suspension does seem to be stiffer on the 2009, so I'll try playing with that on the 2007 a bit.
As I've said, the wobble isn't real bad, but my son is riding this bike and he's a new rider, and if there is something I can do to make it at least as stable as my bike I'd sure like to try.

 

Are you running the front rim lock? I had a shake at high speeds (60ish) not quite a side to side wobble but it could help. I've only experienced a wobbly front with any new tire on tar at very low speeds or when I smoked the front bearings. Watch the rim while riding to see if it's straight. 06 suspension is untouched from when I got it.

 

On the length, were you measuring the axle-to-axle length? The difference might come down to how long the chain is on both bikes...the '07 having a slightly shorter chain. That said, I've never researched the wheelbase length between the two model bikes.