They are armrests. They're not meant to have the driver put weight on them. The sound is probably from the friction between the lid and the storage compartment when you put your weight on it. You can try lubricating the hinge, but that would really only help if the lid was squeaking when being opened or closed.
That's the thing that drives mes crazy. It doesn't even take much weight. lol Maybe ill try the lubrication route. It could be my arm resting on it and shaking as the car is moving idk