Why did the British establish colonies in the Chesapeake and Carolina?
The main reason why the British established colonies in these areas was for money. Most of the colonies from the Chesapeake to the south were established for this reason.
In some of the other regions of the American colonies, colonies were established for other reasons. For example, the Massachusetts colony was established in large part to provide Puritans with a place that they could actually control. This would allow them to make their own religion the official religion. By contrast, the Southern colonies were established mainly to make money. Companies in England funded the colonists who went to the New World to live. They hoped to make money from whatever the colonists could plant or mine or otherwise use.
This distinction is actually somewhat relevant. The Southern colonies attracted very different kinds of people. Since they were meant to simply make money, they were not as attractive to families. Their settlers were often single men. The colonies were also typically dominated by a few rich families. These factors helped make the South very different from the North. It was less democratic and it had more unfree people. These differences would eventually help lead to the Civil War.