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RR is mostly about hysteresis. Reduce hysteresis and you reduce RR. Since roughly 80% of the hysteresis in tires happens in the sidewalls, make the sidewalls stiffer and RR will go down. The easiest way to do so is to increase the pressure. Btw, if you're adding material to make the sidewalls stiffer (same material, just ticker sidewalls), that won't work nearly a well as added pressure. Even though it'll flex less, more material will be flexing so overall hysteresis will pretty much stay unchanged.
Re tread width. It's not about skinny or wide, it's about finding the right contact patch size. Long contact patches from skinny tires increase RR due to increased hysteresis. Make the tread wider and RR goes down, up to a point where RR goes up again.
You can validate that in the graph posted earlier.
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