Going forward, even more changes are on the horizon. On Thursday, Southwest shared a revamp to its Rapid Rewards Credit Cards. Those adjustments involve new perks that are effective immediately, but come with a cost. Each of the five credit cards will have a spike in annual fees .

Chase and Southwest Airlines have refreshed personal and business Rapid Rewards cards, raising annual fees while adding bag, seating and boarding perks. These changes are tied to Southwest's move to assigned seating and paid bags and are accompanied by a limited-time 100,000-point sign-up bonus for personal Rapid Rewards cards.

Southwest's CEO said if the airline had baggage fees at the beginning of the year, they would have led to $1 billion in profit.