Because dark skinned people evolved in hot and humid climates.
Let’s see what happens in cold and dry climate where the Caucasian/white race evolved.
In a dry climate, big lips would get chapped and cracked. Also, the exposed mucosa(wet part) of the lips do not have melanin and hence are more prone to sun damage.
Thick lips. Thick lips are caused by sexual selection. Men find women with thicker lips to be more attractive and signalling more fertility.
In cold climates, sexual selection for thin lips goes in a contradictory direction to natural/environmental selection for the reasons mentioned above.
Whereas in Africa, sexual selection for thick lips is unopposed by natural selection, hence their thicker lips.
Hope this answers your question.