Why there is a resistor soldered across output (green) and excitation (black) in a S-Beam load cell?
The most likely reason is for offset (zero) compensation.

Most Strain-Gauges are relatively low-impedance devices.  Values generally range from 200R through about 1.2k for each of the 4 resistors in the gauges.

You would use a high-value resistor to do this compensation.