Does wheel size have an effect on towing stability?

Question for everyone here: I have been pondering about wheel size and towing stability. I have a 2008 DCLB sport with 17" wheels that I am slowly setting up for towing a 16'-20' down the road. I am considering a different wheel in the future since I am not crazy about the sport wheels. What is everyone's opinions on 16" vs 17" wheel for towing? Assume both would have a regular P- rated tire in stock comparable size. Would the extra sidewall result in a significant amount flex?

 

Negligible difference between a 17" or 16" IMO.

I tow a 23ft travel trailer and am running 265/75/16 in a C load range on my truck. If you go with a passenger rated tire make sure you aren't over the load rating.

 

No, the overall weight and diameter of the wheel and tire combo will have some effect but its all relative, but going from a 16 to a 17 with the same or about the same size tire will make no noticeable difference

 

I notice some amount of "wobble" when I tow my ~4000 lb. travel trailer. The back of the truck just seems to wobble a bit side to side from time to time. It seems ever so slightly squishy. I suspect it is the softness of the P-metric tire side walls. If that is true, then more sidewall would be worse. In my case I plan to swap for LT tires which I think would make more of a difference than 17" wheels would.