Supply and demand, and people prefer non stops so they are in higher demand than connecting flights. If you have direct flights where two airlines are competing on the same or similar lane then that will help, like they do often out of the NY/NJ area.

We adjust our flights usually adding nights on island to save money on air fare, we would rather spend that and a bit more on hotels on island. Those extra nights are also some great times allowing us to try different hotels on island, and at this point I think we have stayed in about 40 different buildings on island and a few over on Anguilla.