[en] As a continuation of our previous work, we investigate the weak decays of doubly-heavy baryons Ξ${}_{Q{Q}^{\mathrm{\prime <!--\; ???\; -->}}}$ into sextet Σ${}_{Q^{\mathrm{\prime <!--\; ???\; -->}}}$ with light-cone sum rules. We calculate the form factors for these decays with the parallel light-cone distribution amplitudes of Σ${}_{Q^{\mathrm{\prime <!--\; ???\; -->}}}$. Numerical results of these form factors are used to predict the decay widths and branching ratios of the corresponding semi-leptonic processes. Parametric uncertainties and theoretical analyses are also given in detail. We find that the decay widths of Ξ${}_{cc}$ and Ξ${}_{bc}$ decays are several orders of magnitude larger than those of Ξ${}_{bb}$ decays.