Here is the policy from SWA's site.
Since 1980, Southwest Airlines has maintained a policy, for purposes of Customer safety and comfort, of requiring a Customer to purchase a second seat if the Customer needs extra space for a large or fragile item, such as a musical instrument, or if the Customer's girth is larger than one aircraft seat. Below are a few points to help clarify our policy:
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Customers who reserve and purchase a discounted, advance purchase fare will be charged the same fare for the second seat, even if the advance purchase requirements are not met at the time of the second seat purchase. A Customer who is holding an unrestricted walk up fare will be charged the appropriate discounted Child's Fare for the second seat.
Once travel has been completed, if the flight is not full, the Customer can request a full refund for the second seat by contacting Southwest Airlines' Customer Relations Department.
This policy was designed to accommodate Customers needing extra space, regardless of the reason (e.g., personal comfort, artwork, child safety seats, large or fragile musical instruments).
The policy is intended to promote the safety and comfort of all Customers onboard and to ensure that no Customers are deprived a portion of the space they have purchased.
