Every airline has different rules published in their contracts of carriage stating under what conditions they might refuse to fly you. As noted earlier, United has a rule governing the transport of passengers who don't fit in a single seat or are so large that they can't lower an arm rest between them and fellow passengers.
Delta has a slightly different set of rules. You can be removed or refused transportation if you can't buckle your seat belt. As with United's contract, no shoes, no service and if you're stinky, it's no go. But in addition, there's a rule about passenger conduct, and it's somewhat vague (no word if it includes two women kissing). Here are the 13 reasons you might not be able to fly on Delta, from Delta's contract:
1) When the passenger’s conduct is disorderly, abusive or violent.
2) When the passenger is barefoot.
3) When the passenger appears to be intoxicated or under the influence of drugs.
4) When the passenger attempts to interfere with any member of the flight crew in the pursuit of his or her duties, or fails to obey the instruction of any member of the flight crew.
5) When the passenger has a contagious disease that may be transmissible to other passengers during the normal course of the flight;
6) When the passenger has a malodorous condition;
7) When the passenger is unable to sit in a seat with the seatbelt fastened;
8) When the passenger requires an onboard stretcher kit;
9) When the passenger’s behavior may be hazardous to himself/herself, the crew, or other passengers;
10) When the passenger is seriously ill, and fails to provide a physician's written permission to fly.
11) When the passenger is traveling in an incubator.
12) When the passenger’s conduct creates an unreasonable risk of offense or annoyance to other passengers.
13) When the passenger’s conduct creates a risk of harm or damage to the carrier’s aircraft and/or property, or the property of other passengers.