Hi group,
The deflection of the meter versus ESR comes from the properties of the unbalanced bridge circuit used in the design. You can adjust the resistor values in the lower legs of the bridge to bend the meter response.
This is an LTspice model that illustrates the effect of changing the resistor value. I have normalized the models to show 0-100% deflection.
These are the results for 1,3 and 10 Ohms:
3 Ohms was chosen the design to give the best scale on the meter, for the majority of applications.
Most electrolytic capacitors have an ESR less than 20 Ohms, if they are good.
Note: this model does not include the non-linearity introduced by the 1N5711 diodes.
It is not easy to adapt the circuit for a 1mA meter.
Jay_Diddy_B