The Cauchy problem for the Hardy–Hénon parabolic equation is studied in the critical and subcritical weighted Lebesgue spaces on the Euclidean space Rd. In earlier works, the well-posedness of singular initial data and the existence of non-radial forward self-similar solutions to the problem were shown for the Hardy and Fujita cases (γ≤0). The weighted spaces are used to treat the potential |x|γ as an increase or decrease in the weight, which enables us to prove the well-posedness of the problem for all γ, with −min{2,d}<γ, including the Hénon case (γ>0). As a by-product of global existence, self-similar solutions to the problem are established for all γ without restrictions. Furthermore, the non-existence of a local solution for supercritical data is also shown. Therefore, our critical exponent, sc is optimal with regard to solvability.