Originally Posted by bulgie

Air pressure holds you up off the ground only indirectly, by tensioning the tire casing, The casing is what holds you up.
Whether rolling or sitting still, the air isn't compressing and uncompressing, it's nearly constant. Totally constant on a smooth surface, only increasing a tiny bit for a brief instant when hitting bumps. That increase is not what holds you up; the tire casing would hold you up just the same even if the pressure didn't go up one bit.

The materials that make a tire have some hysteresis (energy loss from flexing), but especially the rubber — less so in the casing fibers. I'm gonna go out on a limb and predict that energy loss from heating the air in your tire will be below the threshold of "measurable", definitely way below the threshold of "where I start to give a damn".

Energy isn't "returned" to the road, since we don't get energy from the road. (Apologies if that was joshing, I couldn't tell.) I guess theoretically, a bike tire heats the pavement up a little as it passes, but that has got to be the tiniest fraction of where our energy goes. I'm pretty sure all scientists who've studied this agree, almost all the energy that goes into rolling resistance goes into the rubber, via hysteresis.

Bike frames and other metal parts have much lower hysteresis than rubber, which is why flex in frames, cranks, handlebars etc. doesn't waste energy (or not enough to bother mentioning), while tires flexing does.

I disagree with your .sig also! So did Francesco Moser, who set the hour record using probably the heaviest wheels ever used in a bike race. I doubt the heavy wheels helped him much, but they sure didn't seem to hurt.

Man, am I ever argumentative! Sorry about that, science gets my blood up.