Is my Kenwood amp KILLING my poor battery?

It's the same old story. When my system is turned up any more than half way the headlights start dimming to the beat. Dash lights too. The sub hits and my headlights go from white light to dim brown. Aside from beefing up the voltage output with a H/O alternator, and going to a larger battery, I was wondering if just adding a CAPACITOR would help the problem any? we're not talking about a huge audio system here. Just one KAC-7205 amp, one CVR sub and a Alpine H/U. But, the car is a 95 accord. so everything about it is pretty small to begine with. thanks alot for any help you can offer me!