# Weighted histogram analysis method (WHAM) equations

I am struggling in deriving the WHAM equations. Among others, I follow this paper by Kumar et al. In the appendix, in eq. 24 they write the density of states as a weighted sum over the "measured" density of states of different simulations. The weights are $$\omega_j(\{V\})$$. My question is, why are the weights $$V$$-dependent? The same question arises when looking at the Ferrenberg and Swendsen paper (unfortunately not publicly available), in eq. (1). Here they write the weights as $$p_n(S)$$, but again, they are $$S$$-dependent. Why aren't these weights just constant?