In this work, we analyse semi-leptonic and non-leptonic weak decays of the heavy baryons: Λb, Ξb, Ωb and Λc, Ξc, Ωc. For non-leptonic decay modes, we study only the factorizable channels induced by the external W-emission. The two spectator quarks in the baryonic transitions are treated as a diquark and form factors are calculated in the light-front approach. Using the results for form factors, we also calculate some corresponding semi-leptonic and non-leptonic decay widths. We find that our results are comparable with the available experimental data and other theoretical predictions. Decay branching fractions for many channels are found to reach the level 10−3 ∼ 10−2, which is promising for discovery in future measurements at BESIII, LHCb and Belle II. The SU(3) symmetry in semi-leptonic decays is examined and sources of symmetry breaking are discussed.