Soam, you have guessed the phenomenon right. There is correlation between the battery and the music system.
Your music system specs are top-end. The setup certainly saps current from the battery. If you are using music for long time on battery alone, you would potentially drain battery enough to precipitate the situation you describe - A battery low on charge would have internal resistance increased, so if you load the battery more, it would respond by lowering terminal voltage - resulting in dimming of headlamps.
I recommend you use your music system mostly when the car engine is ON, so as not to drain the battery off. I recall here that our ICE legend Arun Dhawan uses his system ALWAYS with the car engine ON, even when the car is parked - because he has a 1000W setup in the car. Your setup is pretty close in wattage.
Also give enough opportunity to your battery to get charged again - looks like your commutes are short, and total use of car less, so the battery does not get a chance to replenish the charge lost. A long drive once in a while will keep it juiced.
And nothing wrong in getting the battery checked. 
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