Until now, it was the only major U.S. airline that allowed passengers to check two bags at no extra cost. On May 28, most passengers will start paying $35 for their first bag.

Southwest Airlines will start charging $35 to check a bag for many passengers on reservations made after May 28.

Earlier this year, Southwest Airlines made the controversial decision to end its longstanding policy of allowing two free checked bags for each customer. However, as the airline implements the policy change this month, it sounds like they will have a major problem on their hands going forward.