Problem of noise with load cell and INA125P + Arduino Uno
You should have a bypass capacitor across the power input (100uF/10V in parallel with 0.1uF ceramic will do), 10n input caps on each input line, as Andy suggests, with series resistors, and I would also suggest a 10n capacitor from reference output to ground. 

If the Ardno and INA125 are separated by more than a few inches, a resistor of at least 1 K on the output of the INA125 and another capacitor from the Ardno input to ground.