If the flight isn't full, they can move to a seat next to an empty one. If the only empty seats are in First Class, they'll have to pay for the upgrade. If none of the above work out, overweight passengers will have to take a later flight and may have to purchase a second seat on that flight.
According to the new policy, anyone needing more than one seat belt extender or who can't put the arm rest down fits into the category.
There's one perk to having to buy two tickets. You can check twice the baggage.
Southwest Airlines has had a similar policy for "Customers of Size" for years.