I've hooked the display up with an Arduino Duemilanove, so the output voltage is 5V.
with a higher-valued resistor the LED should just lit darker" (correct?).
My questions is: Am I measuring wrong?
BKL to be driven by pin1,pin2,or pin15,pin16,or A,K
One way to pick the "right" value would be to use a pot meter (e.g. 100 Ohm in this case) and turn it until you're happy with the backlight level.
If you want to reduce backlight level however, you will still need a series resistor.
Hum.. "LED Forward Voltage" means the voltage it needs to work, right?