Galvanic/voltaic cells - diluting the anode/cathode solution - impact on voltage?

[kingknockout]

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So I did an experiment with the following cell: Zn(s) | Zn+2 (aq, .5M) || Cu (s) | Cu+2 (aq, .5M) When I diluted the cathode solution (Cu+2) to 0.005M, I saw a slight drop in the measured voltage. Is this normal? If so, why? My main question is this: What would happen to the measured voltage if the anode solution (Zn+2) was diluted instead? And why? I don't understand why the dilution of the solutions would affect the measured voltages - I can see how it might affect how long the cell can run, but not the voltage.

[Fortify]

The voltage will decrease as the concentration of the ions in the solution decreases.