  We compute the Chow ring of an arbitrary heavy/light Hassett space
$\bar{M}_{0, w}$. These spaces are moduli spaces of weighted pointed stable
rational curves, where the associated weight vector $w$ consists of only heavy
and light weights. Work of Cavalieri et al. exhibits these spaces as tropical
compactifications of hyperplane arrangement complements. The computation of the
Chow ring then reduces to intersection theory on the toric variety of the
Bergman fan of a graphic matroid. Keel has calculated the Chow ring
$A^*(\bar{M}_{0, n})$ of the moduli space $\bar{M}_{0, n}$ of stable nodal
$n$-marked rational curves; his presentation is in terms of divisor classes of
stable trees of $\mathbb{P}^1$'s having one nodal singularity. Our presentation
of the ideal of relations for the Chow ring $A^*(\bar{M}_{0, w})$ is analogous.
We show that pulling back under Hassett's birational reduction morphism
$\rho_w: \bar{M}_{0, n} \to \bar{M}_{0, w}$ identifies the Chow ring
$A^*(\bar{M}_{0, w})$ with the subring of $A^*(\bar{M}_{0, n})$ generated by
divisors of $w$-stable trees, which are those trees which remain stable in
$\bar{M}_{0, w}$.
