The LCD decoding looks pretty complex due to the 1/3 bias and hence would require capturing 16 lines (maybe 13 if only one of the back-planes is used for timing) at a resolution capable of resolving the levels (and accounting for noise etc) so maybe time to look at the analogue side.
The four load cells (each with 3 wires, Blue/White/Red) are connected to the lower right of the PCB. Looking at the wiring shows the White wires are connected to signals at the PCB whereas the Red and Blue wires simply connect to each other. Further two of the White wire signals go via a small combination of discrete components before reaching the black blob. The arrangement is as follows…
This combination of strain gauges forms a wheatstone bridge (invented by the same person who invented the Playfair cipher system). The essential idea is that an excitation voltage is applied on the top and bottom nodes and the voltage difference across the left and right nodes is measured. When all resistances match there will be no offset however when one or more of the resistances changes there will be a current flow and a potential observed.
In the case of the load cells each load cell contributes two resistors to the circuit making a grid of eight resistors. The Blues are connected to Blues and Reds are connected to Reds. The idea being that when the Reds go up and the Blues go down (remember they are on opposite sides of the load sensor) then the resistances will change and a potential measured.
Measuring the potential whilst the scale is measuring shows a constant 3.76v; so this is the excitation voltage for the load cell bridge. On the output side the White leads go to a pair of resistors each, one 880 Ohms the other 68k Ohms. Pure speculation but that might imply an amplifier stage with a gain of 77.3.