Using a sub-Poissonian optical field generated from a weak twin beam by photon-number resolving post-selection we have simultaneously observed higher-order non-classicalities in photocount moments (sub-Poissonian statistics) and probabilities (witnessed by the Klyshko inequalities). Up to the seventh-order non-classicalities in photocount moments simultaneously with up to the eleventh-order non-classicalities in photocount probabilities have been experimentally observed. Non-classicality counting parameters of different orders as experimental counterparts of the theoretical Lee non-classicality depth have been suggested to quantify and also mutually compare the robustness of these non-classicalities against the noise.