The particle size effects on the charge and spin correlations in half-doped manganite Nd0.5Ca0.5MnO3, which exhibits a charge-ordered (CO) transition at 250 K in the bulk counterpart, have been investigated by magnetometry and electron spin resonance (ESR). Magnetic measurements show that reducing the particle size weakens the long-range CO transition, which completely disappears when the particle size is reduced down to 40 nm. Meanwhile, a weak ferromagnetic (FM) behavior appears at low temperatures and is gradually enhanced with the decrease of the particle size. The ESR intensities of the nanoparticles reproduce well these features. However, the temperature dependences of the ESR g-factor and line width exhibit the typical characteristics of the CO states in all the nanoparticles, even in the 40 nm sample, which suggests that, even though the long-range CO transition is completely suppressed by the size reduction, the CO state is still present in the short-range ordering form. Moreover, it is found that the onset temperatures of the CO states in all the nanoparticles are almost the same as that of the bulk, which strongly indicates that the strength of the CO correlations in this compound is not influenced much by the particle size. A detailed analysis on the magnetic susceptibilities and the ESR line width further reveals that both the antiferromagnetic (AFM) and the FM spin interactions are weakened by the size reduction, which suggests that the enhanced FM behavior in the nanoparticles is not due to the enhancement of the double-exchange FM interactions. We propose that, although the FM interactions are weakened, they gradually dominate over the AFM ones at low temperatures with the decrease of the particle size due to the more significant weakening of the latter by the size reduction, which, hence, gives rise to the development of the FM behaviors in the nanoparticles.