Wouldn't you be adding something in the neighborhood or 100 pounds for sound deadening per that example?
Not unless you tracked in 80 pounds of gravel and dirt while putting the insulation under the carpet. Two rolls of sticky back audio mat would be the heaviest part. The sponge back fiber insulation weighs next to nothing. A couple paint brush servings of contact cement to glue sponge to the backs of the doors isn;t much weight either.
Ten or twenty pounds of sound deadening probably weighs less than the stack of big gulp cups and burger wrappers in most people's trunks. But if that small amount of weight is a problem, buy ear plugs, they weigh a couple ounces.