The influence of capacitors and resistance in a BJT circuit
Gain is determined by the ratio of the collector resistance (actually parallel combination of RL &amp; RC) to the emitter resistance (RE + re).

Where re = 25mV/Ie.

With C3 in place, RE is shorted out as far as the signal is concerned and so the emitter resistance just equals re thereby increasing the gain substantially. RE then just has an effect on the DC bias conditions.

Each of the three capacitors combines with its associated resistance to form three high pass filter. If the three filters all had the same cut-off frequency (f = (1/(2*pi*RC)) then the output would be down 9dB at this cut-off frequency because the three filters are effectively cascaded. To put the response down 3dB at the same cut-off frequency all three capacitors would need to be doubled in value.