Mike, I seriously doubt that the weight of the drywall is causing any problems. Heck, my kids waterbed weights a lot more than that. The only problem with your joists would be finding them if you try the screws that are supposed to go thru the carpet, subfloor, and into the joists. The problem is that the nails are moving in the wood causing the squeek. Even well laid subfloor can have this problem and it is better to put subfloor down with screws. The plywood or OSB sheets can also be rubbing against each other. Stop the movement of the plywood and you stop the squeeks.