It's the larger wheel requires more energy to initially move it. The major factor is the actual circumference of the wheel and tyre compared to the standard. Usually the rim gets bigger and the profile of the tyre smaller so the circumference will stay relatively the same. Having an odd combo such as a 16" wheel with really low profile tyres will cause the speedo to become inaccurate though this only occurs at motorway+ speeds
If the wheel is bigger the tyre will be smaller (assuming the profile of the tyre is adjusted), where does the extra weight come from (more wheel but less tyre)? Maybe from an increase in width?
I honestly can't see how even a relatively large increase in the weight of the wheels and tyres would have any serious effect on the fuel consumption, jack a car up and spin the wheels (at the back on fwd of course), it takes barely any effort at all to spin the wheels, increasing the weight by a few kgs won't make any real difference, and these `heavy wheels' will have lots of inertia that will require less power to keep them turning once they are moving thus saving fuel.
The only area where the weight is really an issue is the effct that increasing the unsprung weight has on handling and performance of the suspension in general.