The voltage between the "signal" output and the circuit's "ground" will be effected by the meter resistance. The DC resistance of the typical milli-Amp meter is about 30Ω, so R14 and the meter resistance form a voltage-divider. With the meter in the circuit, the "output to Audurino" will be a few mV, while without the meter, the open-circuit output could be a couple of volts.
If you want the output to be constant, regardless of the meter being there or not, you will have to switch-in a resistor equal to the resistance of the actual meter you are using.