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.