Converting variable capacitance value to variable DC voltage level
Maybe a linear ramp 555 circuit with an adjustable threshold and a timer chip would do. Here's the linear ramp using the 555: -



"C" in the circuit above could be the capacitor under test. The smaller the value the quicker the ramp. You can use the 555 output rising high to reset-trigger a counter and the counter value can be "frozen" when the ramp reaches a certain level. A precision comparator connected to the ramp would tell you the ramp has reached a certain level. 

If you connect the output of your counter to a DAC and latch the DAC output when the comparator triggers (say 2/3 of way up the ramp) you have a linear, capacitor_to_voltage generator. Adjust R2 to give you the desired range of capacitance you need.

You could also use 7 segment displays to output the counter in hexadecimal.

The counter needs to be running a lot faster than the ramp to give you decent resolution. Anyway, the formulas are on the picture.