  Using the recently introduced multiloop extension of the functional
renormalization group, we compute the magnetic, density, and superconducting
susceptibilities of the two-dimensional Hubbard model at weak coupling and
present a detailed analysis of their evolution with temperature, interaction
strength, and loop order. By breaking down the susceptibilities into
contributions from the bare susceptibility and the individual channels, we
investigate their relative importance as well as the channel interplay. In
particular, we trace the influence of antiferromagnetic fluctuations on the
$d$-wave superconductivity and provide an analytical understanding for the
observed behavior.
