We study the intersection of tropical \(\psi\)-classes on tropical heavy/light Hassett spaces, generalising a result of Kerber-Markwig for \(M^{\operatorname{trop}}_{0, n}\). Our computation reveals that the weight of a maximal cone in an intersection has a combinatorial intepretation in terms of the underlying tropical curve and it is always nonnegative. In particular, our result specialises to that, in top dimension, the tropical intersection product coincides with its classical counterpart.

Mathematics Subject Classifications: 14T90, 14N35

Keywords: Tropical intersection theory, Hassett spaces, \(\psi\)-classes