If, as you seem to indicate, you are on a single ticket for your entire journey, your baggage would be checked from Brussels to Costa Rica, the cost included in the fare, and you would not need to retrieve and re-check during your layover in Atlanta.
Delta's Through-Check Baggage Policy
Effective for travel on or after January 11, 2016, Delta will check a passenger’s baggage between the origin and destination airports that are issued on a single or conjuncted** ticket exclusively. When issued on one ticket, Delta will also continue to check baggage through to the ticketed destination for interline itineraries. If a second ticket is presented for travel, Delta will only check the bag to the destination of the Delta ticket(s). Baggage may be claimed at the De lta-ticketed destination, and then re-checked by the customer with the downline carrier for the next flight.
** A single ticket also means a conjuncted (i.e., conjunctive) ticket. Conjuncted tickets are sequential in number on same ticket stock. It is not possible to conjunct tickets from different airlines.
In cases as noted below, when more than one ticket is presented, Delta will continue to through-check baggage from the origin to the destination.
- An entire journey (itinerary) consisting of Delta-marketed / Delta-operated flights
- SkyMiles Award plus a ticket with Delta-marketed / Delta-operated flights
Delta ticket plus a ticket on the Delta partner airlines listed below:
○ Aeromexico (AM)
○ Air France (AF)
○ Alitalia (AZ)
○ China Eastern (MU)
○ GOL (G3)
○ Jet Airways (9W)
○ KLM (KL)
○ Korean Air (KE)
○ Virgin Atlantic (VS)
○ Virgin Australia (VA)
Delta ticket plus a:
○ SkyTeam pass ticket
○ Ticket with travel on a Visit USA (VUSA) fare
○ Connection to a Delta charter flight
A Facebook chat with Delta Airlines with a similar itinerary and long layover this morning confirmed, since the outbound flights are all on Delta, you do not pick up baggage in the Customs Baggage Claim area in ATL. They will be checked to your final destination. Unfortunately, I'm not finding the options you've suggested for your return flights. It appears they are not all Delta flights, therefore, you would claim and recheck on your return flights.
You may wish to chat directly with Delta about your actual itinerary for confirmation.