In this paper we study the density profiles of self-interacting dark matter (SIDM) haloes spanning the full observable mass range, from dwarf galaxies to galaxy clusters. Using realistic simulations that model the baryonic physics relevant for galaxy formation, we compare the density profiles of haloes simulated with either SIDM or cold and collisionless dark matter (CDM) to those inferred from observations of stellar velocity dispersion, gas rotation curves, weak and strong gravitational lensing, and/or X-ray maps. We make our comparison in terms of the maximal surface density of haloes, circumventing the need for semi-analytic or parametric models for dark matter density profiles. We find that the maximal surface density as a function of halo mass is well reproduced by CDM simulations that include baryons, while for SIDM with a velocity-independent cross-section of 1 cm(2)/g, the simulated galaxy clusters have mean maximal surface densities that are below those of observed systems by an amount greater than the standard deviation of the observed maximal surface density at fixed mass. For less massive systems both CDM and SIDM agree with the observation equally well.