The climate in the tropical regions of the Americas is much worse than in the temperate regions that became the United States. Though malaria, typhus, and other diseases were found in North America, they were absolutely widespread in the Caribbean and South America, so death from disease was much more common much later than further North. Further, the nature of the work being performed was much different. Sugar cultivation and processing is extremely back-breaking labor, particularly the processing. The technologies available in the 18th century required that the people doing the processing work essentially around-the-clock for weeks at a time, which took a toll on their bodies. Combine that with the high prevalence of disease and plantation owners were inclined to make the most out of their investments by working them as hard as possible before they died. Thus, slaves had little chance to live even a semblance of normal lives, including having babies.

Contrast that with rice and tobacco, and later cotton. These are not easy crops to grow, requiring a lot of hard labor. But sugar must be processed on-site and quickly because it spoils, while these other crops were often shipped elsewhere for much of their processing. Slaves in North America had somewhat lighter workloads and MUCH fewer diseases. So they could be allowed to create at least makeshift families and have children.

As for sources, I think much of this comes from Edmund Morgan's American Slavery, American Freedom, but I suspect there are some other sources I'm relying on in there. It's been a few years since I've studied this subject directly. Perhaps my fellow historians can chime in with other ones. If necessary I'll pull out my external hard drive and look through my notes from years back. Let me know and hope this helps!