  We apply a recently developed nonequilibrium real-time renormalization group
method in frequency space to describe nonlinear quantum transport through a
small fermionic quantum system coupled weakly to several reservoirs via spin
and/or orbital fluctuations. We provide an analytic and well-controlled
procedure to solve the RG equations in the weak-coupling regime. Within a
2-loop analysis, we derive analytic formulas for the nonlinear conductance and
the kernel determining the time evolution of the reduced density matrix. Most
importantly, we present a consistent formalism how the RG flow is cut off by
relaxation and dephasing rates, which is necessary to calculate the precise
line shape at resonances. We apply the general formalism to the nonequilibrium
anisotropic Kondo model at finite magnetic field. We consider the weak-coupling
regime, where the maximum of voltage and bare magnetic field is larger than the
Kondo-temperature. In this regime, we calculate the nonlinear conductance, the
magnetic susceptibility, the renormalized spin relaxation and dephasing rates,
and the renormalized g-factor. All quantities are considered up to the first
logarithmic contributions at resonance. Up to a redefinition of the Kondo
temperature, we confirm previous results for the conductance and the magnetic
susceptibility in the isotropic case. In addition, we present a consistent
calculation of the line shape at the resonances, including the determination
which rate cuts off the logarithmic divergence. Furthermore, we calculate the
rates and the renormalized g-factor in nonequilibrium beyond leading order,
being quantities characterizing the exponential decay of the time evolution of
the magnetization. For all quantities we analyse also the anisotropic case and
find interesting nonequilibrium effects at resonance.
