How does impedance analyzer input capacitance influence the measured result?
Actually the capacitors acts as an impedance which influences the circuit.
Impedance, the vector sum of reactance and resistance, describes the phase difference and the ratio
of amplitudes between sinusoidally varying voltage and sinusoidally varying current at a given frequency.
Fourier analysis allows any signal to be constructed from a spectrum of frequencies,
whence the circuit's reaction to the various frequencies may be found.
The reactance of a capacitor is given by:
$$X_c=\frac{1}{2\pi{} f C}$$
$$\pi\approx3.14$$
$$f=frequency  $$
$$C=Capacitance$$ 
As the frequency increases the reactance decreases.
like this capacitance influences the circuit.