Why an does an offset on the reference electrode create an offset on the measure electrode of a pH probe?
The pH probe behaves like a battery, a battery with a very high internal impedance.
One side of the battery is the reference electrode, the other is the measure electrode.
The &quot;battery&quot; voltage is a (fairly linear) function of the pH (and temperature) with 0V output with a neutral solution (pH = 7). Typically the voltage will be something like -400mV near pH = 0 and +400mV near pH = 14. The slope will vary with temperature and with age of the probe.
So the voltage on the measure electrode relative to ground will be the &quot;battery&quot; voltage added to the reference electrode voltage relative to ground.

As to why you might want to use such a configuration- it is so the pH meter can operate from a single supply. By adding a fixed voltage to the bipolar pH probe voltage, everything can be kept positive, which can simplify the circuitry.