Why is it more important to know the amount body fat as opposed to just a person's weight?

Because weight varies from different things such as water intake, muscle mass, etc. When you just focus on the amount of body fat you get a clearer picture. Hope this helps!  

Measuring Body Fat Is Important for Determining Fitness. Weight alone is not a clear indicator of good health because it does not distinguish between pounds that come from body fat and those that come from lean body mass or muscle.

I hope my answer has come to your help. God bless and have a nice day ahead!