Why would anyone want South America?

Britain didn't really have an empire until the 1650s, and even then it only consisted of Jamaica, some territory in India and five plantations in North America. The Spanish and Portugese had been in South, Central and North America since the late 1400s and already had a well-established presence there.

The British did indeed have an interest in Central and South America; the Empire essentially began with privateers harassing Spanish ships and fortresses and looting their gold in the name of the Crown. Sir Walter Raleigh even led an expedition to find El Dorado in the early 1600s, which ended with his execution after his son Wat attacked the Spanish despite James I & VI expressly forbidding such an act.

By the time the British got into North America properly, they had an established presence in India which they were fighting over with both the fractured Indian government and the French as well as West Africa which allowed a lucrative slave trade. Really, North America was a secondary concern; Jamaica and the West Indies were considered the jewels of the Empire, as well as the exploding tea trade from India circa 1700. Our  main interest in America, at the time, was tobacco. Easy to grow, lots of land to attract settlers and indentured labour--as well as slaves--and a native population on the decline due to the introduction of disease.

Source: Niall Ferguson's Empire: How Britain Made the Modern World.

I don't know, maybe the fucking Spanish Empire?

Weren't the Spanish and Portuguese Empires on the decline? I don't know much about the history of Guyana but didn't the British take a chunk of Venezuela from them while they were still under Spanish rule?

Why was the Caribbean considered as jewels when North America was a thousand times bigger with a million times the resources?

It was where the money was; the British didn't have time to expand their operations in North America before the colonists revolted and established the independent republic we all know and love today. It's important to note that, both for the Spanish and British, what had originally been adventuring in the New World for gold and silver quickly turned into a long-run agricultural plan. High hopes were had for North America; Michael Drayton, a contemporary, called it a paradise, while John Smith (yes, that John Smith) thought it held the key for Britain's imperial future. The risks, however, were considerable: the first real settlement, Roanoke, was abandoned in 1586 due to trouble with the natives. Even Jamestown, the first successful British colony in North America by 1609, had a survival rate of around 50pc.

Tobacco is an intensive crop, and the British learned they could grow this around 1612. It ruins the soil within seven years, and while this encouraged a westward spread of settlement, the desire for the Crown to induce emigration to North America meant that no monopoly could be established over North American trade as had been done with corporations like the East India Company, who could control the supply of their good in order to maintain the price and thus the value of the exports to Continental Europe. After all, most of the goods imported to Britain from the colonies were simply exported again to countries like France. This meant that the supply of tobacco increased between 1619 and 1639 to 1.5 million lbs per annum, which led to a price slump from three shillings per lb to just threepence. This was partly due to the ease of growing it, and partly due to the Virginia Company's way of attracting new settlers: significant land, for negligible rent.

The reason Brits kept emigrating to North America was partly spiritual and partly economic. Many Calvinists and Congregationalists decided to flee England after James I decided to uphold Elizabeth's structure of the Anglican Church, which was essentially Lutheran in nature. This was also somewhat encouraged by the government, in order to combat the Popish empire of the Spanish in the region. However, most emigrants to North America were simply responding to their material needs; the Virginia Company advertised heavily, and when the East Anglian textiles industry suffered a depression, it made North America a more attractive opportunity--even if you had to work as indentured labour. The fisheries off Newfoundland and New England also proved incredibly lucrative for Atlantic fishermen.

So, why was the West Indies and Jamaica considered the Jewels of the Empire, prior to the American Revolution? Profit. In 1773, imports from Jamaica were worth five times as much from North America. By 1775, sugar counted for a fifth of the value of all imports to Britain, and were worth five times as much as tobacco. This was due to the explosion of the first consumer economy in the world at the beginning of the 18th Century, with textiles and jewels being in high demand from India and sugar being in high demand from the Caribbean. Tobacco simply never took hold in the way sugar did, and any food production taking place in North America was thought of mainly as being the supply of food that Caribbean monoculture couldn't produce to be self-sufficient. After the Seven Years' War, given the option of either expanding further into North America or retaining the French sugar-producing colony of Guadeloupe, Britain chose the latter. It was simply worth more.