Here's an easy way: figure 1/2 gallon to do 2 good layers on the interior, go to your local auto parts place, pick up a can of herculiner, and your added weight will be no more than that.
In other words, I doubt more than a couple of pounds of weight. If you shed your carpet in return for the insulation and sound deadening properties (not as efficient, but lighter) of the bedliner, then you'll be back to zero or better.