A butt joint of two 10 mm thick stainless steel plates, but 5 mm vertically eccentric to each other, was laser hybrid welded. The weld experiences four point bending fatigue load such that the root stress remains compressive. Thus only the stress formation at the top of the weld was studied, both by fatigue testing and by linear elastic fracture mechanics analysis. The location of the peak stress for crack initiation as well as the direction and speed of crack propagation can be well explained. Weld throat depth, weld toe radii and surface roughness compete against each other for determining the peak stress. It was also shown why occasional lack of fusion has only limited impact on the peak stress and fatigue life. Optimization of the laser beam contribution is responsible for full penetration and for avoiding lack of fusion. Optimization of the MIG-process is essential, as governing the top shape. Beside stress analysis including the topography, the propagation of the cracks along surface resolidification ripples was an indicator that surface roughness has essential impact. Several approaches were developed and studied for systematic documentation and generalization of the discovered knowledge.