Why do my bulbs glow brighter when the microwave is running?
The problem was a bad neutral connection from the transformer on a pole.

I called the power company--they had trucks out to replace the power line within 30 minutes.

Now the power variation is very small.  Without the microwave running, I measure 117.5 volts on the lamp circuit and 118.2 volts on the microwave circuit.  With the microwave running, the voltages go to 118.2 and 114.0 VAC.