Weakly collisional plasmas are subject to nonlinear relaxation processes, which can operate at rates much faster than the particle collision frequencies. This causes the plasma to respond like a magnetised fluid despite having long particle mean free paths. In this Letter the effective collisional mechanisms are modelled in the plasma kinetic equation to produce density, pressure and magnetic-field responses to compare with spacecraft measurements of the solar wind compressive fluctuations at 1 AU. This enables a measurement of the effective mean free path of the solar wind protons, found to be ${≈ }4 \times 10^{5}$ km, which is approximately $10^{3}$ times shorter than the collisional mean free path. These measurements are shown to support the effective fluid behaviour of the solar wind at scales above the proton gyroradius and demonstrate that effective collision processes alter the thermodynamics and transport of weakly collisional plasmas.