I have a Cessna 172S and despite having 4 seats in the cabin, I cannot take 3 more passengers besides myself as the pilot with a full tank of fuel due to safety in weight balance issues. As the pilot, I'm 100 lbs overweight. Hypothetically, we can imagine a situation where a small regional carrier using a turboprop can have only one seat left but the length chord from center of gravity for that seat may cause an unsafe weight balance for the aircraft loading if the passenger is very overweight.

In that case, if not other solution can be found, could the airline reject to passenger for the motive of their weight?