Okay...you asked for it...
It has to do with the ideal gas law. Here's a link if you want to find out more.
Ideal Gas Law
Basically, it is a law that defines how a gas reacts when changes occur in either/all of the following: Pressure, Temperature, and Volume. The formula can be used to calculate changes in any variable from scenario (1) to scenario (2). If the volume remains constant, as in a tire, then the change in pressure will be proprtional to the change in temperature. If temp goes up, then so does pressure. and so on.
Important to note, that to perform these calculations, the temperature has to be converted to the Kelvin scale. If you try to use Fareinheight or Celcius the numbers will be way off.
PV PV
-- = --
T T
(1) (2)
For a motorcycle tire, the Volume is constant as long as you don't get any deformities in your tires such as bubbles/separated belts.
The pressure will change by adding/removing air. As air is added, the Mass is increasing. You are cramming more air molecules into the air space, and since volume remains the same, then pressure will increase. A molecule of air has an atomic weight(mass), so the air mass will change as you add/remove air. This will also change the unsprung weight of the bike, although it is negligible.
Temperature has a large effect on the pressure inside a fixed volume container. Tire manufacturers take this into account when developing the recommended pressures, and why they are always listed as "Cold" pressures. As the tire heats up, then the pressure increases. This also plays a part in tire failure during high speed runs and burnouts due to the heat build up. This raises pressure and also weakens the rubber compound.
Just to throw a wrench into this...Normal air is 21% Oxygen, 78% Nitrogen, and 1% Other. This air will not follow the ideal gas law exactly due to the partial pressures and characterististics of the individual molecules. Nitrogen on the other hand, will act exactly like the ideal gas law. This is why some high performance vehicle will use Nitrogen only in their tires. This includes aircraft tires, but has more to do with the sub-freezing temperatures seen at higher altitudes, than anything else, due to the moisture content in normal air. Moisture will condense out of the air and freeze into ice inside the tire.
I haven't looked at the whole Air vs. Nitrogen thing in a long time, so I may very well be all messed up on that, but the rest of it is correct.
Hope this is what you were looking for, because now my hands are tired.
Remember...you asked.