You could use the good ol' technique of the dynamometer: $$m.g=k\Delta x$$
Where x is the displacement of a spring , k its stiffness coefficient, g the gravitational acceleration (approximately, at the Earth surface) constant 9.81m/s², and m the mass of the weight. Basically place the weight on a spring and read its displacement to get the mass.
You can read the linear displacement however you prefer, the easiest would probably be using a linear potentiometer (e.g. at sparkfun) with the slider tied to the tray. Just measure the voltage of a voltage divider with the potentiometer in it. For more accurate readout, you should make sure the tray is only free to move in one direction (compression of the spring), which is easy to do by attaching flanges to the tray, sliding along walls.
If the maximum displacement of the potentiometer is 20mm and you want to measure from 10 to 100kg, then you should buy a spring with a stiffness of approximately 44.1N/mm.