Thanks for all the great replies.
Definitely have the bug for something lighter that I can take into some remote places. Still not 100% sold on whether it will be a Wee or a KLR, they're both such good choices.
The question to ask yourself is: "Will the bike I choose let me ride comfortably to, and from, the remote places I'd like to explore?"
The KLR is a proven platform for riding remotely with gear. Every single owner I have met claims the KLR is comfortable for some highway use, but in every single encounter I can recall, they rode in using back country routes. Their actions prove the point that the KLR is really not known for it's street manners.
The Wee is a proven platform for touring with gear and it has excellent manners for dirt roads. As you get more remote, the weight becomes a liability. Gets tough to pick up a 500 pound bike once it has decided to take a nap.
With decent off-road oriented tires, crash bars, skid plate, suspension upgrade(s), the Wee can take one to some pretty remote places and in a great deal more comfort than the KLR
There, that settles it. Now all you need to do is decide.