\displaystyle \mathbb E|\mathcal C(u)| \leq \mathbb E_{C_i}\mathbb E\left[|E(u, \overline{W_i})|\,:\, u \in C_i\right] = \mathbb E_{C_i} \frac{|E(W_i, \overline{W_i})|}{|W_i|} = h(W)