  The Kilo-Degree Survey (KiDS) 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 to measure the density profiles and masses of a
sample of $\sim \mathrm{1400}$ spectroscopically identified galaxy groups and
clusters from the Galaxy And Mass Assembly (GAMA) survey. We detect a highly
significant signal (signal-to-noise-ratio $\sim$ 120), allowing us to study the
properties of dark matter haloes over one and a half order of magnitude in
mass, from $M \sim 10^{13}-10^{14.5} h^{-1}\mathrm{M_{\odot}}$. 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 $1.16 \pm 0.13$
(1-sigma) and with the group velocity dispersion as a power-law with slope
$1.89 \pm 0.27$ (1-sigma). 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 (Cosmo-OWLS) project, ruling out models
without AGN feedback.
