Societal issues aside, I'm not sure the airlines really want to deal with actual weights. Especially now with the increase in carry-on luggage, I'll be willing to bet that the FAA averages are well on the low side.

You might make an extra few bucks on the bulkier passengers, but what are the ramifications of having every airplane push several thousand pounds heavier on paper? You can't reduce the thrust for T/O as aggressively, you might end up leaving more people or cargo behind if you're up against the limits - that sort of thing. Perhaps the result would be negligible - I dunno. Just thinking out loud...