How is the brightness of the LED affected by different resistor values?

LED's are light emmitting diodes. diodes have a voltage threshold that must be reached for them to fully "turn on". A resistor can be used to limit that voltage. As the voltage drop across the diode is increased above the turn on voltage (typically .5 - .7 volts), the diode will emmit light. The LED will only light up so far, so by turning the voltage up significantly more will have a very limitted payback in light output.