We derived surface brightness profiles in the g band for 170 Small Magellanic Cloud (SMC) star clusters (SCs) mainly located in the central region of the galaxy. We provide a set of homogeneous structural parameters obtained by fitting Elson-Fall-Freeman and King models. Through a careful analysis of their colour-magnitude diagrams we also supply the ages for a subsample of 134 SCs. For the first time, such a large sample of SCs in the SMC is homogeneously characterized in terms of their sizes, luminosities, and masses, widening the probed region of the parameter space, down to hundreds of solar masses. We used these data to explore the evolution of the SC's structural parameters with time. In particular, we confirm the existence of a physical mechanism that induces an increase of the core radius after 0.3-1.0Gyr. We suggest that cluster mass could be the main parameter driving the inner expansion, as none of the SCs having log(M/M-{sun}_)<=3.5dex analysed in this work undergoes to such an expansion. We also detected a mass-size relationship almost over the entire range of SCs masses investigated here. Finally, our data suggest that globally the SMC SC system is dynamically evolved.