Southwest has a good website and a list of FAQs for customers of size:
http://www.southwest.com/html/customer-service/faqs.html?topic=extra_seat_policy
The answer to the question about what to expect at the airport is of particular help:
Customers of size who purchase one or more seats in advance may check in online or through an E-Ticket Check-in kiosk1 to reserve their boarding positions, but they must see a Customer Service Agent at the gate to receive a Seat Reserved Document. Customers of size who prefer not to purchase an additional seat in advance have the option of purchasing just one seat and then discussing their seating needs with the Customer Service Agent at their departure gate. If it is determined that a second (or third) seat is needed, they will be accommodated with a complimentary additional seat(s).
I think the gate agent would appreciate the customer taking the initiative to ask about this before boarding begins so that things can be addressed.