There are essentially four big issues that have hindered economic development in the Caribbean.
1. The initial colonial situation of small white minorities and large slave populations, which means we start off with just about every island having at least a plurality of the population who are impoverished in comparison with the rest of the country.
2. Relative lack of natural resources- apart from the plantation crops such as Sugar, Rum, Pineapples etc. there are very few natural resources to build an industrial base on for generating income. Jamaica has Bauxite, there's oil in Trinidad, but otherwise most trade goods are based substantially on a small number of administrators and a large number of labourers/temporary workers.
3. Proponderance of natural disasters, whether it be earthquakes, hurricanes or volcanic eruptions that have a habit of knocking the stuffing out of places just when they're getting better.
4. American, and later Soviet, interventionism, which has contributed significantly to creating political instability during the 20th century for Haiti, the Dominican Republic, Grenada and Central America, as well as leading to stuff like the Cuban blockade.
Now, there's stuff which can be done to help here- tourism is starting to see some improvements, Montserrat would be massively better off it the Soufriere Hils eruption of 1995 hadn't led to the evacuation/flight of two thirds of the population, the Haitian Earthquake of 2010 hammered them hard, and Cuba's economy is only just starting to recover from the loss of trade when the USSR collapsed. CariCom is leading to pretty good returns in terms of economic integration across the Caribbean and looks likely to be able to create some transnational investment. Perhaps it the Federation of the West Indies had been made to work it could have helped get a lot of this sorted earlier, but it's a long shot.
Fundamentally though there's just not the space on most of the islands for much manufacturing beyond luxury goods and some agriculture, so what you need is more sustained economic growth in the west to keep the services industry going.