Why do we ground the common probe on a 3 probe liquid level sensor?
The datasheet doesn't explain it but does say


  Level sensor probe volts 5 VAC @ 1.5 mA.


The AC part is to be expected as DC would cause plating of the probes due to electrolysis. 5 V @ 1.5 mA suggests a source impedance of 5 / 1.5m = 3k3.

It then goes on to say


  Adjustable sensitivity: 0 - 50 kV


which doesn't make any sense to me so I'd be interested in learning what this means - if anything.

Meanwhile, back at the earth termination: 


The diagram is suggesting to me that the tank must be earthed (obviously relevant only if metallic) and that the probe should be connected to the tank. I suspect that the tank connection avoids problems with people trying to use painted, galvanized, corroded or limescaled tanks as the common electrode. The diagram on the controller contradicts this by showing only a ground connection to the tank. Who knows?
The datasheet says that the output is isolated from the supply. Ground reference will prevent the output floating and this may be significant to the sensing circuit to avoid stray triggering.


A further confusion with the diagram is that the common probe is higher than the low-level probe. That means that with a plastic tank the low-level indication will be given when the common probe is dry rather than when the low-level probe is dry. All-in-all, it's not very satisfactory documentation.

Note that the supplier has been inconsistent