It's an FAA reg that an airline must operate a scheduled flight, even if it has zero passengers booked. Plus, the airline needs the aircraft in the downstream cities anyway. I never understand why people immediately assume an airline cancels a flight just because its empty.
First I think you are the one being foolish if you think any airline is going to run an completley empty flight unless they need the crew in the next city. Secondly I have had gate agents in DCA tell me to my face "the load was to low" so they bumped everyone to the next flight. Even if an FAA rule exists that says that "you must fly" it would be very hard to enforce since there are such a vast variety of reasons an airline can claim under "operational" delays.