I am not an expert but often times the getting brighter indicates a loose neutral somewhere.
Have the POCO check their connections and have an electrician check yours.

Brightening is caused by a loose neutral connection.
Unplug you electronics and call the POCO right away.
You also should call an electrician.
The POCO may find no problem on their side (location depends on jurisdiction) but the problem needs to be corrected immediately.
It can cause damage and fires.

Without a neutral the balance between the two 120V legs can wander all over the place and even approach 240 V on a 120V circuit.
240 V loads are NOT affected unless they also need 120 V.

I guess that pretty well sums up the severity of such a situation! Brickeye, where it only happens on the one circuit, doesn't that pretty well eliminate the POCO side of things? And could the loose neutral be anywhere in the affected circuit? So everything on that circuit from the main panel connection to the last receptacle on that circuit would need to be checked?

If it is only on a single circuit look for a multi-wire circuit.
This is a pair of 120 V legs feeding two circuits.
The two legs share a single neutral, and if the neutral becomes disconnected then the 120 V between the legs can move around depending on exactly how much load is on each leg.

What happens is that the two 120V circuits are acting as a single 240 V circuit.
If the loads on each side are exactly the same, the midpoint stays at ~ 0 volts.
If the loads are not exactly the same the mid-point moves away from 0 volts.
Multi-wire circuits may have a common trip circuit breaker, but not all are required to.
If you do not understand how they work, or are not comfortable working n a panel board, call an electrician.
You should avoid using the two circuits.

Great explanation and I believe I actually understand what you're saying. I'm probably way oversimplifying this, but basically the neutral is used to keep each of the legs in balance and prevent an overvoltage situation on one of the legs?

The neutral provides a reference for the middle of the 240 V winding on the pole transformer.
In the actual circuit it carries the difference in the to halves of the winding to keep the split 50-50 at 120 V per leg.
Loose the neutral on a circuit and you get an uneven split (except in VERY rare cases- like perfectly matched resistive loads).