Kinda reply to many posts here, as i just did this on my K2. (Assuming proper rim width) The widest tire to fit is 150. It won't hit the chain but it will hit the chainGUARD, which will have to be notched or displaced. The popular harley 16" conversions are 150 widths, no problem, except for the guard.
Wider requires moving the mount point of the brake arm outwards. The brake arm is the stay that extends from the front right of the underneath of the swingarm and travels back to the brake plate, wher it keeps it from rotateing. You can simply pull the arm out of the U that it fits in, and put it on the outside of the U and run a proper spaced bolt in it. half arsed but it works. Or you can cut the inside leaf of the U off and reweld it to the outside, giving the brake arm a proper berth. This will allow out to 170, then you'll likely hit the chain.
I've settled on a 140/70-17 on a 3.50 rim. I'll likely go to 150 at first replacement. I moved my stay mount just in case.
You do not need Carpy's swingarm, IMO.