I'm sure you meant diameter width = 195 or 205 in this case. 60 is the profile [rim to tread] & a 205 is quite a bit wider then the stock 180. A 195/60-16 is very close to stock. Just a bit wider.
I'm pretty sure Ken meant diameter. You're right that the "60" is the profile [rim to tread]. The "60" is really the aspect ratio of sidewall height to tread width meaning the sidewall height is 60% of the tread width.
For the stock 180/70-16, the width is 180mm and the sidewall height is (180mm x .70) = 126mm.
For a 205/60-16, the sidewall height is (205mm x .60) = 123mm - 3mm shorter in radius / 6mm shorter in diameter.
A 195/60-16 will be 9mm shorter in radius / 18mm shorter in diameter.