Understanding the physical mechanisms at the origin of slow slip events has been proven a very challenging task. In particular little is known on the role of fault heterogeneity during slow slip. In this study we provide evidence that fault fabric controls slip velocity time histories during slow slip events generated in the laboratory under the specific boundary condition of imposing a stiffness ratio K=k/kc~1. We have performed experiments using a double-direct biaxial shear apparatus and two different fault gouges, homogeneous quartz powder and heterogeneous anhydrite/dolomite mixture. We measure fine details of fault slip to resolve the slip velocity time history and volumetric deformation that, coupled with an analysis of the resulting microstructure, allow us to infer the mechanical processes at play. Our results show that slow slip events can be generated for both fault gouges when k~kc with similar values of breakdown work. The shear fabric exerts a strong influence during the co-seismic breakdown stage of instabilities. In quartz, where most of the slip occurs on a localized (1 µm) slipping surface, the peak slip velocity is attained near the final stage of friction breakdown and therefore a relevant amount of the mechanical work is absorbed during slip acceleration to peak slip velocity. In anhydrite/dolomite mixture, the peak slip velocity is suddenly reached after a relatively small drop in friction, accompanied by fault dilation, implying that most of the mechanical work is absorbed during slip deceleration. For anhydrite/dolomite mixture these results are likely related to heterogeneous slip distribution along the observed foliation. Taken together these observations suggest that the mechanics of slow slip events depends on shear zone fabric. The slip velocity function contains the necessary dynamic information to characterize the evolution of shear stress. The data are uploaded are structured as follow: 1) a .txt file of the datafile that is recorded from the machine (raw data) 2) a reduction file (_r) that is used to elaborate the raw data 3) a file in .txt format containing the elaborated data (data_rp) The data are analyzed using rawPy that can be found at https://github.com/marcoscuderi/rawPy For any additional information please do not hesitate to contact the corresponding author Marco Maria Scuderi at marco.scuderi@uniroma1.it.