The authors identify a class of weight functions \(\varphi:\mathbb C^n\rightarrow\mathbb R\) which have the following property: if the Hankel operator \(H_{\psi}:A^{2}(\mathbb C^n;\varphi)\rightarrow L^{2}(\mathbb C^n;\varphi)\) is bounded, then \(H_{\psi}:A^{2}(\mathbb C^n;\varepsilon\varphi) \rightarrow L^{2}(\mathbb C^n;\varphi)\) is Hilbert–Schmidt for every \(\varepsilon\in (0,1/2)\). Here, \(L^{2}(\mathbb C^n;\varphi)\) is the space of square integrable functions with respect to the measure \(\exp(-\varphi(z))\text{d}\lambda(z)\), \(\lambda\) being the Lebesgue measure on \(\mathbb C^n\). \(A^{2}(\mathbb C^n;\varphi)\), the weighted Bergman space, is the intersection of \(L^{2}(\mathbb C^n;\varphi)\) with the space of entire functions. This result allows to obtain the compactness of Hankel operators for symbols \(\psi\) which are not necessarily bounded.