1993 Mercury Tracer

When I bought the 1993 tracer, I had problems running at night. When I used my lights with or without my stereo, and would accelerate, the light would dim and it would drain my battery. I was told it was my alternator, so I replaced that, ran fine for a month or two, then did it again, so I tightened the belts and it ran fine, now another month or so later, it is doing it again. The car runs when I disconnect the battery so my alternator is running, could I have a short somewhere from my battery to my car? I cant figure out whats wrong, again when I accelerate at night it dims my lights, stereo cut outs, n my battery drains, when I park its dead, completely. If u need me to explain more I can, I jus am lost