Fat One
 

Hey Jamski,
What width 17inch rims do black one and bleue have to run

Rear - Dunlop 150/60 ZR D207 E Sport Radial (Sport Max II)
Front - Dunlop 120/60 ZR 17 D204 F

Rear - Michelin 160/60 ZR 17
Front - Metzeler 120/60 ZR 17

As I have got an 84 xt600 and can't seem to find what the maximum width rim I can run on it.

Not tried much else, but got Distanzias on my 88 bike, and they work just fine on the road. Like everyone else above has said, dont muck about putting fat tyres on thin rims. You squeeze the sidewalls in and completely change the profile of the tyre, often resulting in less rubber on the road than with the proper size tyres.
If you want fat tyres, and dont ride on the dirt , stick a pair of 17 inch rims on.

rim to tyre chart
Rim to Tyre Application Chart

I'm tempted to fit a 140/80 17 to my xt660z, in an attempt to get more mile's out of a K60 on my Africa trip next year. I'm not too concerned about cornering, but on a straight road, there must be more rubber touching the road, no?

be carefull with the clearance... some larger tires than stock WILL HIT the swingarm at the Shock linkage!

I once fitted 140/80 knobbies with 20mm threadpattern (Mefo-sport mfc12 "stonemater"). Fitted fine. Guess you can fit a 108 link chain instead of a 106 link, so you can use the snailadjusters to move the whole wheel back as much as possible.

I might have had a 108 link chain at the time, dont remember, sorry.