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We present the evolution of galaxy size and surface brightness in the rest-frame J band (1.22 μm), tracing the stellar mass distribution, over 0.5 ≤ z ≤ 3, using a sample of 15,420 galaxies with stellar masses M⋆ = 1010–1011.5M⊙ from the JWST COSMOS-Web survey. The rest-frame J-band effective radius (Re,J) is obtained from previous measurements and mapped from the available JWST/NIRCam filters, while the surface brightness (μJ) is corrected for dust extinction and cosmological dimming. At a characteristic mass of M⋆ = 5 × 1010M⊙, star-forming galaxies (SFGs) exhibit a size evolution of Re,J ∝ (1 + z)β with β = −0.92 ± 0.04, falling between previously reported shallower and steeper measurements. Quiescent galaxies evolve more rapidly, with β = −1.34 ± 0.05, consistent with earlier studies. Among SFGs, lower-mass systems (1010–1010.5M⊙) show slower (β = −0.66 ± 0.02) size evolution compared to their higher-mass counterparts. Furthermore, the surface brightness brightens toward higher redshifts, scaling as (Formula presented) μJ∝−2.5log(1+z)γ. We find γ = 3.07 ± 0.08 for SFGs and γ = 3.70 ± 0.08 for quiescent galaxies. We also find that massive SFGs (M⋆ > 1010.5 M⊙) exhibit similar μJ values at fixed redshift, independent of mass. Finally, we demonstrate that the observed surface brightness evolution is driven by the combined evolution of galaxy luminosity and size.