For the tire pressure to go up when the bike weight is on the tire versus on the center stand, the volume of the tire has to decrease. If the pressure doesn't change, that means the volume of the tire is not decreasing and the shape of the tire is changing when weight is added but not decreasing the internal volume of the tire.
In the case of a shock, the internal volume is getting smaller when weight is added to the bike and therefore the pressure goes up.