Well, the story I used to hear is that blacks are all descended from Cain, that black skin is the “mark of Cain,” and that his descendants were to have this “mark” as well. Then someone pointed out that Cain’s mark was supposed to protect him from harm. (Who was supposed to harm him when Adam & Eve were the only other humans on Earth? :rolleyes 
By inference, whites were supposed to be descended from other children Adam & Eve had after losing Cain & Abel. I never heard who the ancestors of Asians were supposed to be. One of Noah’s three sons, maybe?
As far as the shape of Asian eyes, it’s also supposed to protect the eye from freezing and minimize the glare of sunlight off of snow. Thus, it may have originated among the first inhabitants of Mongolia and Siberia.
Finally, there is supposed to be a connection between skin color and the body’s ability to produce Vitamin D from sunlight. In Equatorial regions where the days and nights are of nearly-equal length all year long, dark skin is needed for protection from ultra-violet light, but this reduces the efficiency of Vitamin D production. But since there is an abundance of sunlight year-round, the body is still able to produce enough of the vitamin. A balance between protection and the need for Vitamin D exists.
In the far north or south, one does not need dark skin because of the relative weakness of sunlight. However, the lack of sunlight would mean a concurrent lack of Vitamin D for dark-skinned people. Those who were not born with light skin would perish from Vitamin D deficiency. Those who WERE born light-skinned remained healthy, were able to hunt and gather food and live to pass on their mutated trait to their offspring.
If American Indians are (mostly)* descended from Asians who crossed the Bering sea, this stil applies. It seems obvious to me their reddish skin tone is a mutation of the yellowish skin tone of Asians, a mutation necessary to endure the more intense sunlight of the Americas, which are of lower latitiudes than the bulk of Asia. Also, the climate here tends to be more sunny.
*I say “mostly” because there is new evidence that Europeans may have successfully crossed the Atlantic more than 23,000 years ago. They may have interbred with the Asians who may have crossed the Bering Strait (or used boats to follow the North Pacific coastline) far earlier than we thought. I mentioned this before on another thread, and if the Search Engine works, I’ll find it. Wish me luck.
When all else fails, ask Cecil.