I haven't personally acquired and read through this, but perhaps this would provide some insight:
http://papers.sae.org/760732/
I'd also be a bit wary of the study or understanding you're trying to undertake. I'll give some insight from my recollection of several years at Goodyear's world headquarters:
Say you're developing a tire line with a matrix of different sizes - bead diameters, widths, overall diameters, whatever. There are only a handful of "development sizes" sprinkled throughout that matrix that get the up front design work. Gets expensive with each mold iteration you cut being $30,000-50,000! You'll have at least one vehicle platform that you track test these on. Maybe multiple if you've got say a 15" and 18" bead diameter tire in the same tire line.
Do all the design work to try and hit your subjective handling targets on each development size, noise, wear, durability, etc. Then the rest of the sizes are more or less "interpolated" from there. So as what trend you get, that may be entirely contingent on the particular tire line, how the development sizes were done, and whatever company policy is as far as interpolating between sizes.
Can also be dependent on the vehicle platform you're using and load range you're in. Just like sometimes adding air pressure will increase cornering stiffness, sometimes decrease it...
Grip is a four letter word. All opinions are my own and not those of current or previous employers.
