The "get off my plane!" incident illustrates yet another reason why air travel during the holidays is insanity. The total weight of the cargo isn't known until the plane is loaded, and during Christmas, everybody checks packages, like two new bowling balls for cousin Billy, bags of pink cement for aunt Hattie, etc. So they could reach takeoff weight limits, but they won't know for sure until they see if the plane fills up. Under normal circumstances, the takeoff limits would almost never be reached.
There are two other considerations that affect weight and balance limitations. Weather enroute or at the destination could influence the airline to load more reserve fuel than is normally required (the minimum is allowing for 45 extra minutes aloft on domestic flights). Also, density altitude considerations could mean that a plane can no longer take off with a given weight if the temperature has risen substantially (takeoff distance is longer with hotter, less dense air). Flights that originate in or stop in Denver can be affected by this problem (actual altitude+increased density altitude). Oh, and if the winds aloft forecast changes, the projected amount of fuel needed could rise.
Given that modern airliners are designed with a generous amount of wiggle room insofar as their design limitations are concerned, I suspect that you could stuff a plane full of fat people and have everyone check two 35 lb. bags and everything would actually be just swell. But CYA and "better safe than sorry" are good policies.