Tire Pressure?

No, PSI is PSI, the tires may bulge more or not be flat on the bottom when on or off the ground but the PSI is the same unless you were to exceed the tires ability to expand than the force of the weight of the car could increase the PSI. The biggest difference you will encounter IMO is changes of temperature, I can have a 5-8 psi difference from cold 4am 42 degree pressure to mid day 75 degree and warm tires

 

Maybe someone doing their own tire swap over the next few days can check this out?

I've thought about this (idly, never followed through and checked), when I've checked tire pressures before install. I'd suspect an unloaded, off the vehicle tire/rim would have slightly lower pressure. Might be negligible.

 

The same amount of gas is in the tire. The only way the pressure is going to increase is to decrease the volume of the tire. I will bet the usual amount that sitting on the ground or sitting on a lift makes no difference.

 

Pressure will increase but you probably won't be able to measure the difference with an ordinary tire gauge.

The reason it will increase is as load is increased the tire distorts and that reduces inside volume by a very small amount.