A variety of factors caused slavery to rise in the Southern colonies between 1619 and 1670. These included factors in the colonies themselves and factors elsewhere. Let us examine a few of these factors.
Perhaps the most important factor in the rise of slavery was the rise of tobacco as a major crop in the South. Tobacco was very labor intensive and needed a great deal of attention. It would have been impossible for tobacco to boom in the way that it did had there not been a large workforce made up of unfree laborers.
A second factor was one that arose in England, not in the colonies. In England, economic conditions improved over the time period in this question. This reduced the flow of indentured servants to the colonies. While indentured servitude was not as bad as slavery, few people would have opted to become indentured servants if they really had other good choices. As the economy in England improved, people had more choices and were therefore less likely to indenture themselves. This meant that African slaves became more important as a source of labor.
Finally, there was some worry about having too many ex-indentured servants in the colonies. Powerful colonial elites worried that the ex-servants would be hostile to them. They worried that they would, in essence, engage in class warfare against the elites. African slaves were better, then, because they would never be freed and would never form a lower class hostile to the upper classes.
All of these reasons helped to bring about an increase in slavery over the course of the 18th century.