When considering whether or not it causes the gun to become "out of balance", it should be considered first whether or not the gun was built and left the maker with one. I have an AE 30" 16 ga. Fox that was shipped with a Silvers pad. It does not have it now, but the old pad was replaced somewhere along the way with a hard rubber buttplate. It will be going back to the way it was originally built soon, and I fully expect it to handle perfectly.
But, yes, thick solid rubber pads are heavy. I have no accurate scales on which to weigh any of my stash. I have a couple of new London Silvers on hand, and they are noticeably heavy. The ventilated ones ...... Hawkins, most of the Jostams, etc. will be lighter than the Silvers style, usually. You would have to remove a fitted pad from a gun and weigh it. Weighing a new, unground pad would be erroneous.
SRH