Capacitive sensing can employ a parametric amplification scheme. That means, the developed signal depends not on an input voltage or current, but on a
parameter of the apparatus (in this case, the capacitance being sensed).
One can balance an AC bridge containing a pair of matched capacitors.
The excitation of the bridge with an AC reference will cause zero
developed signal across the output, because of the matched condition,
but a nonzero signal if there is a capacitance change.
simulate this circuit – Schematic created using CircuitLab
Here, for example, note that the speaker will give minimum sound output
only when the capacitors match; any change in the sensor capacitance results
in an audible indication of the imbalance. More elaborate schemes are possible, and there's almost no limit to the sensitivity of such an apparatus (your signal drive can be increased, or frequency modified, or output signal amplified).
Adjust a calibrated trim capacitor for minimum sound (signal output), and
you have measured the sensor capacitance. Alternately, use synchronous
rectification and differential amplification instead of a speaker, and
read out the capacitance difference on a voltmeter.
Even a very small capacitance change can be sensed reliably.