If Africa is where humans evolved, why isn't it the most populated part of the world?

People are not stagnant. 

I am pretty certain that the people now living in that region stayed and kicked the rest of us out of there. History has shown us that when you are content and well fed you stagnate. 

DNA and fossils. The reason the populations of China and India boomed was because of the domestication of rice and wet agriculture growing practices (obviously different than the climate of Africa and the plant crops in Africa).

Biologists believe early human ancestors started out with light skin. Even most mammals have light skin. Dark skin probably evolved after humans lost their body fur because naked skin was vulnerable to UV radiation as explained in the out of Africa hypothesis. Dark skin people literally came from light skin people. 💪🏻✊🏻

Because much of Africa is too dry for farming. Agriculture was invented after the end of the last ice age, 10,000 years ago, in the Middle East and in China. Before the invention of agriculture, humans were hunter gatherers everywhere around the world, and people had to hunt and gather plants to stay alive. Meat rots quickly after an animal is killed, so it cannot be used to sustain a large population. Before the invention of agriculture, human population density was low everywhere on earth. 

In contrast, agriculture can produce lots of surplus food that can be stored (with the help of cats catching mice), and the domestication of animals (many are fed with grain grown by farmers) also provide a good reliable source of meat. Because of agriculture, some human populations boomed. India and China have over a billion people each, because of agriculture.  In contrast, much of Europe is not suitable for agriculture and so there are only 1/3 as many people in Europe as there is in India. Many Indians are descendants of Middle Eastern farmers, and so are most north Africans. China experienced a population boom and many Chinese migrated to SE Asia. Before agriculture, SE Asia was populated by dark skinned,  curly haired people who migrated out of Africa 60,000 years ago. Some of them (known as Negritoes) are still around but they are now a minority in countries like Malaysia and the Philippines. The light skinned Chinese migrants took dark skinned native wives at first but as the number of people carrying Chinese genes increased, they started picking wives that looked more like their ancestors back in China. That is why today there are a lot of SE Asians who look just like the Chinese, with light skin and straight hair, but some do have features that resemble Africans, such as darker skin, fuller lips and wider noses. 

The same thing happened to India. Middle Eastern farmers who were descended from Europeans migrated to India and they did the same things the Chinese did, taking dark skinned natives as wives and then as time went by, their descendants preferred lighter skinned people who share light skinned ancestors with them. The migration of European farmers to southern Africa only took place within the past few hundred years, and southern Africa is not as good for farming as either China or India.South Africa had a severe drought a few years back. In fact, humans migrated out of Africa 60,000 years ago because of a severe drought and a shortage of food. Before then there was no non-Africans. All non-Africans are descendants of a small group of Africans who migrated out of Africa 60,000 years ago. 

Agriculture was practiced in ancient Egypt by people who migrated there from the Middle East. It was possible because of the Nile River providing the water needed. Elsewhere in Africa, people did not know how to practice agriculture and there was no suitable sources of water for irrigation. In contrast, there are many major rivers in China that can provide irrigation, and there are also many rivers and streams in much of SE Asia and India. The Middle East itself it a lot drier so there are also fewer people in the Middle East than in China and India, despite having expertise in agriculture and irrigation. 

The sub-Saharan African region experiences disproportionate rates of infectious and chronic diseases in comparison to other global regions.

because most of Africa's wealth/food was/is "exported"

Population levels reflect resources available. Much of Africa is resource poor leading to small numbers of nomadic people ranging over a large area. The early modern humans who migrated into Eurasia found a much more resource rich environment, allowing the population to become more settled. This in turn lead to animal domestication and the advent of agriculture, from hat point on the Eurasian population exploded while Africa's population remained more nomadic and relatively smaller.