  We determine the spin susceptibility $\chi$ in the weak interaction regime of
a tunable, high quality, two-dimensional electron system in a GaAs/AlGaAs
heterostructure. The band structure effects, modifying mass and g-factor, are
carefully taken into accounts since they become appreciable for the large
electron densities of the weak interaction regime. When properly normalized,
$\chi$ decreases monotonically from 3 to 1.1 with increasing density over our
experimental range from 0.1 to $4\times10^{11} cm^{-2}$. In the high density
limit, $\chi$ tends correctly towards $\chi\to 1$ and compare well with recent
theory.
