I've never been in a situation where I felt my great mass reduced the performance of the KLR. I'm 6'4" and when I bought it, I weighed around 300. In fact, for my size, it's one of the most comfortable motorcycles I've ever ridden. I'm down to about 270 now, but it seems for every pound I lose, I find another pound of crap to haul around on the bike that I think I might need and use some day. I'm sure I might see a difference if I weighed 100 pounds less, but that ain't gonna happen.
I did install raising links in the rear to give the rear shock a little advantage since the loss of a little suspension travel doesn't matter much with my riding. I plan to upgrade the shock one of these days. It'll handle you just fine.