No expensive measuring pads needed.
The heavier the aircraft, the closer to the ground it will be.
A laser light installed on the bottom of the fuselage at or near C. of G. should be able to give a reasonably accurate distance to the tarmac.
This type of laser, found quickly with the help of Mr Google, gives an accuracy to 2mm:
Laser Sensor Applications » Blog Archive » Drill Depth Measurement » Laser Sensor Applications
Obviously, an apparatus developed specifically for aircraft use would be even more accurate.
I imagine an a/c overloaded by 20,000lbs would compress it's main oleo's by more than 2mm.
It would not be hard to develop tables calculating the "ride height", if you will, for all weight conditions from empty to maximum allowable.
If the laser measurement distance on an overloaded a/c shows less than that allowed for an entered condition.......no pushback.
I thank the "Dambusters", and their downward triangulated spotlights for this idea.