There are at least two reasons why the population grew more quickly in New England than in the South.
First, there was the fact that the South was dominated by plantations that were worked by slaves. This meant that most people who were considering immigrating to America did not want to go to the Southern colonies. These people generally wanted to own their own land and be able to farm. They did not want to have to compete with plantations owned by wealthy people and worked by slaves.
Secondly, it is important that New England was settled by families while the Southern colonies were more often settled by single people. This mattered for two reasons. For one thing, it meant that there was likely to be less procreation in the South as there were not ready-made families in that area. For another thing, the South had more single men and was therefore a more violent environment than New England. The lower rates of birth and higher rates of death (death rate was helped along by the fact that there were more diseases like malaria in the South) caused there to be less natural increase in the Southern population. This, combined with lesser immigration, meant that the overall population grew more slowly in the South.