Black widows are extreme millisecond pulsar binaries where the pulsar wind ablates their low-mass companion stars. Their optical light curves vary periodically due to the high irradiation and tidal distortion of the companion, which allows us to infer the binary parameters. We present simultaneous multi-band observations obtained with the HIPERCAM instrument at the 10.4-m GTC telescope for six of these systems. The combination of this five-band fast photometer with the world's largest optical telescope enables us to inspect the light curve range near minima. We present the first light curve for PSR J1641+8049, as well as attain a significant increase in signal-to-noise and cadence compared with previous publications for the remaining 5 targets: PSR J0023+0923, PSR J0251+2606, PSR J0636+5129, PSR J0952-0607 and PSR J1544+4937. We report on the results of the light curve modelling with the Icarus code for all six systems, which reveals some of the hottest and densest companion stars known. We compare the parameters derived with the limited but steadily growing black widow population for which optical modelling is available. We find some expected correlations, such as that between the companion star mean density and the orbital period of the system, but also a puzzling positive correlation between the orbital inclination and the irradiation temperature of the companion. We propose such a correlation would arise if pulsars with magnetic axis orthogonal to their spin axis are capable of irradiating their companions to a higher degree.