Pull-up resistor over a microphone
The reason there's a pull-up resistor is to supply power to the built-in FET impedance converter:



The mic diaphragm itself doesn't need any bias, since it's an electret mic.  "Electret" means "permanently electrically charged".  So the diaphragm is always already biased, even without any power applied.  So the resistor and bias voltage has no effect on the frequency response or other properties of the diaphragm.  

The resistor value does affect the gain of the FET, however, since this is a common source amplifier.  Increasing the resistor (within reason) will increase the output voltage level.

(and 1 kilohm is not a high resistor value.  If the diaphragm was not electret, you'd need to supply your own bias to it, through a resistor, and for minimal self-noise, this is typically in the gigaohm range, which is 1 million times as large.)