[meew0]

Humans are 3D objects, but fat is not distributed equally throughout the body. Most fat is subcutaneous fat, i.e. located right below the skin. Its abundance can therefore be approximated by body surface area, which is proportional to height squared.

[naniwaduni]

This might be a nice explanation of it didn't fail to agree empirically with reality, where in fact there is a significant cubic component which gives rise to the "something close to the 2.5th power" that GP suggests.