ABSTRACT Scaling relations trace the formation and evolution of galaxy clusters. We exploited multi-wavelength surveys – the XXL survey at XMM-Newton in the X-ray band, and the Hyper Suprime-Cam Subaru Strategic Program for optical weak lensing – to study an X-ray selected, complete sample of clusters and groups. The scalings of gas mass, temperature, and soft-band X-ray luminosity with the weak lensing mass show imprints of radiative cooling and active galactic nucleus feedback in groups. From the multi-variate analysis, we found some evidence for steeper than self-similar slopes for gas mass ($β _{m_\text{g}|m}=1.73 ± 0.80$) and luminosity (βl|m = 1.91 ± 0.94) and a nearly self-similar slope for the temperature (βt|m = 0.78 ± 0.43). Intrinsic scatters of X-ray properties appear to be positively correlated at a fixed mass (median correlation factor $ρ _{X_1X_2|m}∼ 0.34$) due to dynamical state and merger history of the haloes. Positive correlations with the weak lensing mass (median correlation factor $ρ _{m_\text{wl}X|m}∼ 0.35$) can be connected to triaxiality and orientation. Comparison of weak lensing and hydrostatic masses suggests a small role played by non-thermal pressure support ($9± 17{{\ \rm per\ cent}}$).