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May be it is time I step into this discussion:
RRC: By definition it is the rolling resistance divided by the load. However, when it is quoted as a value, RRC means the value obtained in a test divided by the test load. Typically, the test load is the rated load (the one written on the sidewall) - which is hardly ever the load the tire sees in service.
BUT..... you can't determine the RR by taking RRC and multiplying by the actual load on the tire. RR is not proportional to the load, and while it is also not linear, it is pretty close. (I'll have to look up some typical response surfaces and post them later if folks are interested.)
This brings us back to the tire size problem. If a particular tire has a particular RRC, if you were to measure the same identical tire in a different size, you would find it has a different RRC. In general, the RRC value is most closely related to the load carrying capacity - and as a general rule, larger rim diameters have larger load carrying capacities.
It's been found that even if you keep everything the same, larger capacity tires are "More Efficient", but their RR values are higher (meaning not proportionally so.)
So beware of tires that quote RRC by itself. You need more information if you are to figure out what a particular tire is going to do in a different size.
Which brings me to the originally posted question:
IF the tires were the same diameter, but the rim diameters were larger, AND the load carrying capacity was the same, AND everything else were exactly the same: the tire would be wider in cross section (the first number in the tire size), the tire would be lower in aspect ration (the second number in the tire size) and as stated in the initial conditions, the rim diameter would be larger (the 3rd number in the tire size) - something like this: 175/70R13 -> 185/65R14 -> 195/60R15 (Sharp eyed readers will note that is rule of thumb doesn't quite work, but generally, this is how it works.)
With that in mind: Going larger in rim diameter results in more RR, because the tread width would be wider: more tread = more RR.
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