What has a greater effect on fuel efficiency as far as wheels and tyres are concerned? Is it the width or the diameter?
Here's something to bear in mind when wheels and tyres are concerned - weight and diameter can directly influence momentum.
For any given speed, an increase in either will increase momentum. This means more torque will be needed and hence more fuel will be consumed by the engine.
Unless a larger diameter wheel is of a lightweight design, upsizing will affect fuel economy adversely. But moving up one size, for example, from 17 to 18 inches is, not likely to cause a significant deterioration in fuel efficiency.
An example of how a manufacturer enhances fuel efficiency can be seen in BMW's choice of wheels and tyres for its electric i3. They are lightweight 19-inch units, but they are shod with tyres that are unusually narrow. Having narrow tyres has two advantages - reduced rolling resistance and minimal frontal area and hence lower air resistance.
But it is hard to say whether wheel size or tyre width has the bigger influence on efficiency.