Tire size calculator
If you plug in 225/60/16 as the stock size and 235/60/17 as the new tire, you get a tire with a sidewall 0.3" taller and therefore 1/2" more in diameter.
Yes, that is a useful tool, but you can get erroneous results. Not all tires in a given size have the same dimensions - sometimes there are significant differences.
If you really want to understand the sizing, you need to go to Tire Rack or the manufacturer's websites, and look up the dimensions you are interested in on their "Specifications" pages. It takes a little time, but the results can be educational.
The Cooper is 28.3 inches OD and 9.6 inches section width. Tread depth 12.5/32 inches
The Yoko is 27.6 inches OD and 9.1 inches section width. Tread depth 12/32 inches.
So the Cooper is actually 0.7 inches taller and 0.5 inches wider, but that is actually pretty close to what the tire calculator predicted...... however, sometimes it isn't that accurate.
You need to look up your OEM tire size at Tire Rack and see what the (unworn) figures are, and then you can compare and see what effect the two new tires will have.
I wouldn't go any wider than stock unless you absolutely need the floatation, and I would only increase the OD a little (2 or 3%) to avoid performance losses and speedometer error.
Weight is another consideration - a heavier tire will be more robust, but you take a hit in terms of rolling resistance and mpgs.... and sometimes it is very hard to find tire weights. Cooper does NOT publish them on their website, and it may take a phone call or email to get an answer. I had to call and play phone tag to find the weight of my (very heavy) STT tires.
BTW, I like the look of the Cooper - it is the successor to the very good ATR. Maybe you should buy that one so you can give us a road test report....
Spokane WA USA