Can an airline reject a passenger for being overweight? 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?
Yes.  If carriage of said person on a particular flight would cause the aircraft to be overloaded or outside of its CG envelope, the airline has full right to refuse them passage for safety reasons. It would be illegal under Part 121 and Part 135 to do otherwise.

Practically speaking though, most large commercial aircraft have such great payloads that this would not happen on a frequent basis.  Now the airlines may charge said person for an additional seat costs because of their size and girth.