That's normal. Tiny engine, with a tiny alternator it's bound to happen. My 2K Civic does that. You could look into getting a higher output alternator. That would 'fix' it.

 

I think what you describe in normal. my headlights dim when I roll up or down the windows. I just got a reman alt and other problems have vanished as a result. i think you should be concerned with your alt if your headlights brighten when you step on the gas.

 

Clean all your grounds, check the battery terminals for corrosion, and maybe check the output voltage of your alternator. A healthy one should be 13.8 to 14.4V. If its down are 12 that's your problem.