Having worked in the Air Express business for 15 years I can tell you that we knew what packages would go on the plane and what wouldn't before we loaded the containers. We found the passenger lines to be close to clueless on this right up to the departure time. I've always written it off to a different focus, but really this is simple math and they should know before people show up to the airport...... send an SMS message or make an outbound call - "we're bumping you from this flight due to weight restrictions"
Of course, here's the touchy part: do you bump one rev customer that weighs 350 or two 175 pounders? I wouldn't want to be engaged in that conversation!