This paper presents the results of our experiments with weak incident shocks diffracting over concave corners. For Mach reflexion, the experiments reveal a fundamental difference between weak and strong shock diffraction, namely that for weak shock diffraction the corner signal can always catch up with the three-shock confluence, but this does not happen for strong shock diffraction except for comparatively small corner angles. We show that by taking into account the attenuating effect of the corner signal it is possible in principle to modify the well-known von Neumann theory and that this is then in good agreement with the experimental data. Evidence is presented which shows that another effect of the corner signal is to cause a partial loss of the self-similarity property of the three-shock system. Indeed, for one series of experiments the oncoming flow relative to the Mach stem behaved as though it were parallel to the sloping wall of the corner and therefore did not have the familiar radial distribution centred on the corner. The modified theory can be extended to include the persisted regular reflexion phenomenon suggesting that this is an unresolved Mach reflexion. In that event there is some experimental evidence that transition to Mach reflexion would then be consistent with the normal shock point as Henderson and Lozzi found for strong shock diffraction.