This might help a bit, but I think you're still going to have problems with a dog the size of a Newfie.
American Airlines
American Airlines (aa.com) only allows one dog kennel per ticketed passenger in the main cabin, and like many other airlines, the total weight of the dog and kennel together cannot exceed 20 pounds. But the weight limit of a single dog, its kennel and all accompanying contents, such as toys, food and water bowls, increases to 100 pounds when traveling as checked baggage in the cargo section of the plane. If, on the other hand, that same kennel has two dogs, the total weight limit drops back down to 20 pounds, with age restrictions dictating each dog be between 8 weeks and 6 months old. The cost is $125 per kennel.
Air Canada
Air Canada (aircanada.com) flights have a maximum allowable weight of 22 pounds -- dog and kennel -- in the main cabin, but up to 70 pounds when checked as cargo. But the size of the kennel must be no more than 115 inches when the length, width and height are added together. The per-kennel cargo cost is $105. Dogs checked as cargo do not need to be accompanied by an onboard passenger and will be admitted into Maple Leaf Lounges so long as they are kept in their kennel at all times. In addition, Air Canada requires a health certificate and proof of immunization before checking any dog onto a flight.
Alaska Airlines (I have no idea if they serve Costa Rica)
Alaska Airlines (alaskaair.com) has some of the most relaxed weight restrictions in the industry, partly because many Alaska residents own extremely large canines. While in-cabin weight limits are comparable with American Airlines, dog and kennel together can weigh up to 150 pounds when checked into the baggage compartment. Additionally, a 500 size kennel is the largest allowed on any flight, with maximum dimensions of 30 inches by 27 inches by 40 inches. A $100 fee is assessed each way. When the combined weight is 151 pounds or more, the airline has a special Air Cargo division that will make arrangements and offer alternative pricing.
Delta Airlines
Delta Airlines (delta.com) permits 400 and 500 series kennels with maximum weights of 24 and 31 pounds, respectively, to be checked as cargo on all aircraft. An extra-large 700 series kennel with a maximum weight of 51 pounds is permitted on some flights. Rates for these kennels range from $85 to $180. But dogs are not admitted into the baggage area on any flights between May 15 and Sept. 15 because of extreme heat or between Nov. 1 and March 31 on Utah, Idaho and Wyoming flights because of severe cold. As an alternative though, dog owners can take advantage of the Pet First program, with specifically designated aircraft used for shipping pets year-round.
United Airlines
United Airlines (united.com) will accept 400 and 500 size kennels on all aircraft for $145 and $160, respectively, while 700 size kennels are permitted only on larger Boeing aircraft for $250. All dogs, regardless of size, are accepted as cargo at United's SPD/QuickPak counters, but are no longer accepted at passenger ticket counters unless they qualify for the military and State Department exceptions policy. Under the PetSafe program, passengers have access to a 24-hour live animal help desk and weather condition monitoring at all points of the flight; plus, climate-controlled transport is used between connecting flights if the dog will be exposed to temperatures in excess of 85 degrees.
Cheers,
James  Expat-blog Experts Team