Carol,

I can't speak for any other locations but my personal experience has been the non-stop flights out of JFK to St. Maarten are the cheapest, be they AA or JB. Not familiar with Delta so not sure about them. I once asked a reservation specialist why this was so and his best explanation (beyond "I'm really not a hundred percent certain.....") was that once you get into connecting from NY through different states and multiple airports there are extra taxes and airport usage fees involved whereby the direct flight only has one set of taxes.