2000 Ford Contour Flickering lights

I have a 2000 ford contour V6 and I seem to be having a problem with my headlights. As soon as I turn my lights on they begin to flicker (not flashing because they never go out) But they go from bright to dim. Along with that my check battery light comes on and goes off while I'm driving in unison with the flickering of the lights. I had my battery check so I don't believe it is the problem. Also when I turn on my A/C the air flow changes when the lights go dim and bright. For Example, when the lights go dim the air flow isn't as strong, but when they go bright the air flow is stronger. Do you have any idea what kind of problem this could be? If so I would appreciate the help! Thanks!