For the plain strings it's really the pitch that determines rate of change, not the string thickness. I'm only taking about the 3 plain strings. (Core to wrap mass ratio affects the wound strings.)
Try the simple test I described. Tune the B or even the high E down to G, the usual pitch of the 3rd string. (Ideally this would use a locking nut and equal saddle position/height but you can skip that part if you want.)
After retuning, do you think the 2nd or 1st string will change pitch more slowly than the 3rd string with bar use, because they're so much thinner? How much more slowly? Assuming the 3-2-1 semitone thing happened at G-B-E, do they still rise that amount and reach Bb, A, Ab together?
You need to make one attribute (pitch or string thickness) equal in a test to determine how much the other one actually matters.