In order to prominently investigate the effects of the surface spin on the magnetic properties, the weak magnetic ZnLa0.02Fe1.98O4 nanoparticles were chosen as studying objects which benefit to reduce as possibly the effects of interparticle dipolar interaction and crystalline anisotropy energies. By annealing the undiluted and diluted ZnLa0.02Fe1.98O4 nanoparticles at different temperatures, we observed the rich variations of magnetic ordering states (superparamagnetism, weak ferromagnetism, and paramagnetism). The magnetic properties can be well understood by considering the effects of the surface spin of the magnetic nanoparticles. Our results indicate that in the nano-sized magnets with weak magnetism, the surface spin plays a crucial rule in the magnetic properties.