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Within 24 hours of your departure, you can tell us how many bags you will check and pay any fees quickly and easily online. That means one less thing you will have to do at the airport. When you arrive at the airport, you can drop off your checked baggage at the nearest baggage drop, marked with red "Baggage Drop" signage, or curbside check-in station (available within 6 hours of departure time). You may also check your bags at the airport kiosk, ticket counter, or curbside.

Traveling light is always ideal, but it's not always realistic. The best advice we can give as far as minimizing fees is to pack as efficiently as possible and learn where it will cost you. If you plan on exceeding the standard baggage allowance, here is everything you need to know about quantities, extra fees and restrictions.
Before we get to all the nitty-gritties, please note the following general guidelines:

Up to 10 bags may be checked per passenger on flights operated by Delta and up to four total checked bags on Delta Connection® carrier flights.
We may limit the amount of excess baggage when such excess prevents us from transporting up to two bags per passenger.
Delta Connection carriers accept excess baggage on a space-available basis. If the baggage cannot be carried on the same flight with you, it will be transported on the next available flight.
Camera, film, videotape, lighting, and sound equipment will be accepted when tendered by representatives of network or local television broadcasting companies or commercial filmmaking companies. See Media Bags for complete details.

Additional, overweight and oversized baggage is accepted on a standby basis.
Bags that do not meet our size and weight restrictions will require special handling and additional fees.

Excess Baggage | Delta Baggage | Delta Air Lines

اعتقد أن هناك خطأ بالحجز أو أن الموظف لا يعرف أنه يسمح لك بحمل حقيبة واحدة على خطوط دلتا وهو موضح هنا من موقع دلتا

Checked Baggage | Delta Air Lines