Evidence of beam loading due to distributed injection in Plasma Wakefield Accelerator experiments carried out at the FACET facility at SLAC during the year 2012 is presented. The source of the injected charge is tunnel ionization of Rb+ inside the wake, which occurs along the length of the interaction at each minima of envelope betatron oscillation. Rb was used specifically to mitigate the problem of head erosion, which limited the energy gain in earlier experiments using Li that were carried out at FFTB in SLAC. In the present experiment however, electrons produced via secondary ionization of Rb were injected in the wake and led to a severe depletion of the accelerating wake, i.e. beam loading, which is observed as a reduction of mean, i.e. measured, transformer ratio. This "dark current" limitation on the maximum achievable accelerating gradient is also pertinent to other heavier ions that are potential candidates for high-gradient PWFA. Show Partial Abstract