Potential energy stored during the inter-seismic period by tectonic loading around faults is released during earthquakes as radiated energy, frictional dissipation and fracture energy. The latter is of first importance since it is expected to control the nucleation, the propagation and the arrest of the seismic rupture. On one side, the seismological fracture energy estimated for natural earthquakes (commonly called breakdown work) ranges between 1 J/m2 and tens of MJ/m2 for the largest events, and shows a clear slip dependence. On the other side, recent experimental studies highlighted that, concerning rupture experiments, fracture energy is a material property (energy required to break the fault interface) independently of the size of the event, i.e. of the seismic slip. To reconcile these contradictory observations and definitions, we performed stick-slip experiments, as analog for earthquakes, in a bi-axial shear configuration. We estimated fracture energy through both Linear Elastic Fracture Mechanics (LEFM) and a Cohesive Zone Model (CZM) and through the integration of the near-fault stress-slip evolution. We show that, at the scale of our experiments, fault weakening is divided into a near-tip weakening, corresponding to an energy of few J/m2, consistent with the one estimated through LEFM and CZM, and a long-tailed weakening corresponding to a larger energy not localized at the rupture tip, increasing with slip. Through numerical simulations, we demonstrate that only near-tip weakening controls the rupture initiation and that long-tailed weakening can enhance slip during rupture propagation and allow the rupture to overcome stress heterogeneity along the fault. We conclude that the origin of the seismological estimates of breakdown work could be related to the energy dissipated in the long-tailed weakening rather than to the one dissipated near the tip.