Heater causing the car to have power loss

Hello, I have a 2000 ford escort zx2. Whenever I'm driving it and turn the heat on the car seems to have a slight loss of power to the motor, then returns to normal. It does this on and off every 30 seconds or so while I'm driving. Sometimes if I'm going uphill it acts like it wants to downshift or something, it shutters really hard. I recently changed the oil/filter, air filter, fuel filter, added Lucas injector cleaner, trans filter, a battery terminal, ball joint, sway bar link, and cleaned the throttle body(tho I didn't remove it to do so). The car runs so much more smoother but still has the problem when I turn on the heater, and occasionally shutters uphill(a lot less now than before). Could this just be a vacuum leak? And if so which one?
On another note I have hooked up a 500watt amp and 13" subwoofer. Could this have to do with any of my problems, and should I replace the normal battery with a bigger one? Any suggestions will help, thank you!