Animals count as carry-on items. The combined weight of the pet and carrier may not exceed 20 pounds. The pet must remain inside their dog or cat travel crate (17-by-8.5-by-12.5 inches) while at the airport and in the aircraft for the entire flight.
How do you fly a big dog in a cabin?
A 40-pound dog is indeed too large to travel in-cabin on most (if not all) airlines and will have to ride as cargo. Besides very small pets, only trained and certified service or support dogs with legitimate documentation can sometimes accompany their owners in-cabin.