Each person traveling with Southwest Airlines Baggage Policy is permitted to check two complimentary baggage, each no more than fifty pounds in weight and sixty-two inches (L+W+H). There is a $75 cost for overweight (51-100 pounds) and big (62-80 inches) luggage. Also allowed are one carry-on bag and one personal item per passenger. Their website has specific criteria for unusual baggage, such as musical instruments and sporting equipment.e permitted for carry-on luggage. They have more standards and a list of prohibited items on their website. Wheelchairs and strollers, for example, are free of charge when they meet certain criteria.