Welcome. If you haven't read it, here's an excerpt from my "New KLR Owner Mistakes to Avoid" list;
2) Chain tension: many owners and some shops overtighten the KLR's drive chain; due to the long travel suspension and geometry the KLR needs more slack than other bikes people may be used to. If the chain is too tight you risk damaging the countershaft seal and bearing as well as possibly the wheel bearings along with premature wear of the drive chain and sprockets. Quick check; with the bike on the sidestand, you should be able to touch the chain to the bottom rearmost portion of the chain slipper but not the metal swingarm itself.
Basically the tightest point is when the swingarm is in alignment; the rear axle, front swingarm pivot and countershaft and as long as you still have some slack at that point, you're good. Weight makes no difference; a lighter rider will still move through that tight spot as the suspension cycles.
The proper way to make sure you have enough slack is to put the bike on a stand, remove the rear suspension linkage rods (dog bones) and move the wheel up until the three points have aligned as I described above, making sure there is still some slack. Alternatively people have used ratchet straps to compress the suspension to that alignment point.