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 $4times10^{11} cm^{-2}$. In the high density limit, $chi$ tends correctly towards $chito 1$ and compare well with recent theory.
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