In many ways, sugar made the British West Indies what they are today.  Sugar was the major driver of the West Indian economy.  Perhaps more importantly, it was because of sugar that African slaves were brought to the West Indies, where their descendants are the dominant ethnic group today.

In the mid-to-late 1600s, sugar became the major crop in the Caribbean.  Needing workers to staff the sugar plantations, the British started to import large numbers of slaves from Africa.  For example, this link tell us that the island of Barbados went from having only a few hundred slaves in 1640 to having 20,000 in 1650.  By the end of the century, the slave population was up to 80,000.

This sugar economy led to a society in which there were huge numbers of black slaves ruled by a relatively small white population.  At the apex of this society were the rich white plantation owners.  This has meant, of course, that much of West Indian culture has been tremendously impacted by the cultures brought over by African slaves.  Thus, the sugar economy had (and continues to have) a huge impact on West Indian culture.

How did sugar growing affect British West Indian society and rice growing affect South Carolina?

These two lucrative cash crops introduced into British colonies in the Caribbean and in the South Carolina marshlands were labor intensive crops that required a lot of water and a lot of land.  African slaves quickly became the dominant source of this labor, and in South Carolina particularly because slaves stolen from West Africa already knew how to grow rice.

The large number of these slaves created an interesting cultural mix of African and English languages, customs and beliefs, with some native dialects and traditions blended in.

Charleston, South Carolina quickly became the largest slave market in North America, and Barbados in the Caribbean became the largest market there, in order to feed the sugar, spice, tobacco and rice cash crop plantations that made up most of the British imperial economy.