Starting on Wednesday, the Dallas-based carrier will charge customers $35 for their first checked bag and $45 for their second checked bag. The bag fee change will also apply to existing flight itineraries changed on or after May 28, Southwest confirmed to "Good Morning America."

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.