© 2015 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. The Kilo-Degree Survey is an optical wide-field survey designed to map the matter distribution in the Universe using weak gravitational lensing. In this paper, we use these data tomeasure the density profiles and masses of a sample of ~1400 spectroscopically identified galaxy groups and clusters from the Galaxy And Mass Assembly survey. We detect a highly significant signal (signal-to-noise-ratio ~120), allowing us to study the properties of dark matter haloes over one and a half order of magnitude in mass, from M ~ 1013-1014.5 h-1M⊙. We interpret the results for various subsamples of groups using a halo model framework which accounts for the mis-centring of the brightest cluster galaxy (used as the tracer of the group centre) with respect to the centre of the group's dark matter halo. We find that the density profiles of the haloes are well described by an NFW profile with concentrations that agree with predictions from numerical simulations. In addition, we constrain scaling relations between the mass and a number of observable group properties. We find that the mass scales with the total r-band luminosity as a power law with slope 1.16 ± 0.13 (1σ) and with the group velocity dispersion as a power law with slope 1.89 ± 0.27 (1σ). Finally, we demonstrate the potential of weak lensing studies of groups to discriminate between models of baryonic feedback at group scales by comparing our results with the predictions from the Cosmo-OverWhelmingly Large Simulations project, ruling out models without AGN feedback.