A primary field in Conformal Field Theory transforms as $$\phi (z,\bar{z}) =\left(\frac{dz}{dz'} \right)^h \left(\frac{d\bar{z}}{d\bar{z}'} \right)^\bar{h}\phi (z',\bar{z}') $$ under a conformal transformation.
I read in chapter 2 page 41 in Strings, Conformal Fields and M-theory by M.Kaku that $h+\bar{h}$ is called a conformal weight and $h-\bar{h}$ a conformal spin.
What is the motivation, especially for the spin-one, for these names?