Delta has a new baggage offer that could help ease the onboard roller derby for overhead space.

Beginning June 1, Delta American Express affinity cardholders will be able to check one bag free on Delta. Delta currently charges $25 each way to check a bag, so you could save $50 each time you fly round-trip if you have the card. The offer extends to up to nine people flying on the same reservation, so if you have a family of four, you could save as much as $200 round trip.

Even with this offer, you'll want to pack light; Delta charges $35 each way for the second bag.

The annual fee for the cards starts at $95, but those fees could easily be made up if you fly several times a year or if you travel with family.

In addition to the baggage perk, airlines often offer affinity card sign-up bonuses. You'll also earn miles for your everyday purchases, and the annual fee sometimes is waived for the first year.

Continental has been offering a similar deal to its Chase affinity credit-card holders since last fall. The airline also waives the fee for the first checked bag for Continental Chase debit-card holders.

The question is why the airlines would offer free bags when they generate so much revenue from bag fees. The answer is that they probably get a sign-up bonus from the card companies for new cardholders. Also, 75 percent of people fly only once a year, but the airline can get a piece of the profits from the cardholders' purchases all year long.

This new baggage offer could put a pinch on Southwest, which had a selling point of offering two free checked bags to any passenger. JetBlue offers one free checked bag.