In your “bag over the limit” example, the bag being weighed is going under the aircraft in the bulk cargo compartment. THOSE bags are weighed, because the density of materials carried in the cargo holds varies immensely.
Baggage going INSIDE THE CABIN is not weighed and considered part of the “average weight of the passengers” calculation. Fat, thin, heavy, light INSIDE the aircraft averages out. In the fuel tanks and cargo hold, where you are carrying hundreds of thousands of pounds of weight, it’s slightly more important, because as fuel burns off, the weight distribution changes.
300 pax & bags is about 60,000lbs that stays relatively still. 100,000lbs of fuel burned doesn’t. Throw in the heavy cargo in the multiple cargo compartments, with each box/bag being different weights/densities, and that weight distribution is slightly more important.
For every 300lber & bag there’s probably a kid or a 100lber…all becomes a relative wash.