The same mentality used to apply in the West. Rich people could afford to be indoors and under shelter even outside. Having the palest skin was a status thing. Having a tan became a sign of status because people with wealth could afford holidays, even if were a couple of weeks in some Spanish resort. A similar change occurred with obesity.

Having a bit of extra weight has at various times been seen as a sign of wealth, as poorer people were less likely to be fat due to a lack of food combined with the need to work in physical jobs and walk everywhere. In modern times obesity is more the preserve of the poor due to an abundance of cheap high-calorie food, lacking time to exercise, and less education on taking care of ones physical condition. These two points suggest that racism isn't necessarily a nice and easy answer to why some non-white cultures value lighter skin. It's far more complex than that and plays out in many different ways, such as the north-south divides in Italy and Spain.

Edit: elaborated on the race aspect and added obesity.