For the sake of extendable industry applications, weldability of magnesium-strengthened aluminum alloy 5083H116 thick plate is discussed to comprehensively unravel why mechanical properties are fluctuant and bring about an opportunity to well understand transport phenomena, solidification behavior, phase equilibria and elasticity-plasticity development. Each individual process plays all-important role in quality and process control. Physically, laser is intensely concentrated on material to increase massive vaporization of alloying elements, and it is energetically favorable for hourglass-shaped full penetration weld. There is a competition between preferential magnesium vaporization loss and excessive eutectic reaction. Under the circumstances, both inappropriately contribute to onset of metallurgical and mechanical properties instability. α-Al solid solution and Al3Mg2 β phase are intermixed. The morphology, size, distribution and amount of metastable eutectic β phase are asymmetrically pertinent to thermo-solutal convection of laminar or turbulent flow in the overheating weld pool. Fluid flow redirects between counterclockwise convection and clockwise convection, while weld pool is melted and subsequently solidified. The mechanism of non-equilibrium eutectic β phase transformation as a consequence of asymmetric heat input is briefly proposed. Size, distribution and amount of Al3Mg2 β phase at neck transition region are parabolically boosted in the partial penetration weld. In contrast, size, distribution and amount of Al3Mg2 β phase at bottom part are monotonically augmented in the full penetration weld. Although welding parameters are unvaried for all experiments, mechanical properties of weld are diverse, and there are noticeable differences between welds and base material. Because of heterogeneous resistance to weld failure, unpredictable weld pool hydrodynamics, plasma gas dynamics, grain growth kinetics and phase transformation thermodynamics ahead of vapor/liquid or liquid/solid interface hinder convergence of experiment data, directly or indirectly. This heat sensitive and reflective material not only is capable of significant residual stress and distortion, but also is susceptible to formidable metallurgical defects in the slender keyhole, and both reduce strength, ductility and toughness of weld for expedition of intergranular fracture. Conclusively, in order to elucidate response of material to welding conditions, this phenomenological methodology provides solid foundation for multivariable optimization to suppress weld defects, lessen eutectic reaction, meliorate microstructure integrity, alleviate weldability problems and safely improve reproducibility as well as controllability through viable enhancement of metallurgical and mechanical driving forces for fracture-resistant weld in the laser material processing.