  We present numerical simulations of the growth and saturation of the
Kelvin-Helmholtz instability in a compressible fluid layer with and without a
weak magnetic field. In the absence of a magnetic field, the instability
generates a single eddy which flattens the velocity profile, stabilizing it
against further perturbations. Adding a weak magnetic field - weak in the sense
that it has almost no effect on the linear instability - leads to a complex
flow morphology driven by MHD forces and to enhanced broadening of the layer,
due to Maxwell stresses. We corroborate earlier studies which showed that
magnetic fields destroy the large scale eddy structure through periodic cycles
of windup and resistive decay, but we show that the rate of decay decreases
with decreasing plasma resistivity, at least within the range of resistivity
accessible to our simulations. Magnetization increases the efficiency of
momentum transport, and the transport increases with decreasing resistivity.
