Malaria and yellow fever were introduced to the Caribbean from Africa in the mid-17th century. They quickly became endemic.

West African populations carry a genetic trait that increases their resistance to malaria, and many Africans brought to America as slaves had also survived yellow fever and so were resistant to that as well. They fared much better, and had more children, than European colonists, who died in droves.

These diseases shaped Caribbean history in many ways. A British expedition to conquer Mexico in 1741 lost 20,000 of its 27,000 members in short order. Napoleon's attempt to hold Haiti and by extension Louisiana failed due to yellow fever, which wiped out 50,000 of his soldiers. Santa Anna became president of Mexico in part because of his birth in Veracruz, which gave him and his followers a significant military advantage due to their resistance to the area's endemic yellow fever.

There simply were little reasons for White Europeans to settle in smaller Caribbean islands like , say, Barbados, Dominique or Nevis. Lack of economic opportunity (most vacancies were for back-breaking plantation workers or military garrison) and hot climate.

However in bigger Caribbean islands of Cuba, Hispaniola (Dominican rep. and Haiti) and Puerto Rico there were and are large European population. Haiti in Hispaniola used to have large population of Europeans and free blacks, before most of them migrated to Louisiana and France following the Haitian revolutions. These bigger islands could support more diverse economy and bigger population

Many Historians divide European Imperialism into Settlement Colonialism and Extractive Colonialism (my awkward terms).

Settlements were first and foremost taken for living space, and were settled by large groups of Europeans who wished to more or less continue their lifestyle in a new, less crowded place, and stay there for a long time. Settlement colonies were almost always founded in places that had climates similar to Europe, where the settlers could use traditional farming techniques and avoid tropical diseases. This is why you have large white populations in Argentina, South Africa and most of North America.

Extractive colonies on the other hand were not primarily conquered to live in, but rather to extract resources. Tropical areas had lots of stuff Europeans wanted, but they couldnt sustain European farming techniques and were filled with diseases Europeans were vulnerable to. These places usually had a European ruling elite (who generally just wanted to make some money and then go back home) but were populated by natives or slaves imported from other tropical areas.

The Caribbean islands generally were extractive colonies, although as others have mentioned some islands did have extensive European settlement

Thanks for the informative and interesting answer guys.