Have you ever been driving on a road slick with ice or rain and noticed that your had a death grip on the steering wheel with white knuckles and tense shoulders? That death grip doesn't translate into more control over the car. Same goes for how you use your hands when working out.
You don't need to grip the weights as if you were trying to squeeze the life out of the dumbbell or hold the handles of the elliptical like you are trying to choke them. All this really does is tire out all the little muscles in your hands. Since these muscles are small and relatively weak compared to the larger muscles you are intending to work, they just tire out before your workout is done. This can create unwanted soreness in your hands. Plus, having an overly tight hand often sends signals of tension to the shoulders and neck, creating unnecessary strain.
I see this super grip when folks work with Pilates equipment, weight and cardio machines, and free weights. Next time you work out, check your grip and lighten it up.