Can I add extra baggage for my customer when I book a flight, or do they have to buy it at the airport?

Yes, in most cases you can add extra baggage during the booking, though how much you can add and when depends on the airline and on the supplier that flight comes from.

When flight results come back, the included baggage allowance is shown wherever the airline shares it, so you can see at a glance whether a cabin bag only fare or a fare with checked luggage is being quoted. On the passenger details step, any paid baggage the airline makes available for sale will appear as an option you can pick before you confirm, and the cost is added to the total your customer pays. This works well for low cost airlines, because selling bags in the booking flow is how they normally operate.

The honest limit is that not every airline opens baggage sales through its API. Some full service carriers already include luggage in the fare and offer nothing extra to buy at booking time. Others sell bags only on their own website or at check in, and a few release the option after the ticket is issued rather than during the booking. In those cases the booking goes through without a baggage choice, and your customer buys the bag later, usually at a higher cost than it would have been in advance.

If you need to add luggage to a ticket that is already issued, raise it as a change request from the booking screen so your team keeps a record of it, and anything you add is saved against the booking for your staff to see. Before you promise a client anything, run a test search on the airlines you sell most and check whether the baggage option shows up for them.