brother they surely do affect car handling and road feed back for sure.
i have experienced it first hand once i switched the size on my margallah from 175/70/13 to 195/50/15.
the over all tyre dimensions once translated are exactly same (almost) however i can assure you that the road feed back is so much different.
Autophile brother is correct since he has also shared the details with 4.1% increase (over all) in the wheel + plus tyre size which means the height of the car has increased further, which is not a very good thing in the already very high new corolla.