Radial mass-to-light ratio gradients cause the half-mass and half-light radii of galaxies to differ, potentially biasing studies that use half-light radii. Here we present the largest catalog to date of galaxy half-mass radii at z>1: 7006 galaxies in the CANDELS fields at 1.0<=z<=2.5. The sample includes both star-forming and quiescent galaxies with stellar masses 9.0<=log(M_*_/M_{sun}_)<=11.5. We test three methods for calculating half-mass radii from multiband PSF-matched Hubble Space Telescope (HST) imaging: two based on spatially resolved spectral energy distribution modeling, and one that uses a rest-frame color profile. All three methods agree, with scatter <~0.3dex. In agreement with previous studies, most galaxies in our sample have negative color gradients (the centers are redder than the outskirts, and r_e,mass_<r_e,light_). We find that color gradient strength has significant trends with increasing stellar mass, half-light radius, U-V color, and stellar mass surface density. These trends have not been seen before at z>1. Furthermore, color gradients of star-forming and quiescent galaxies show a similar redshift evolution: they are flat at z>~2, then steeply decrease as redshift decreases. This affects the galaxy mass-size relation. The normalizations of the star-forming and quiescent r_mass_-M_*_ relations are 10%-40% smaller than the corresponding r_light_-M_*_ relations; the slopes are ~0.1-0.3dex shallower. Finally, the half-mass radii of star-forming and quiescent galaxies at M_*_=10^10.5^M_{sun}_ only grow by ~1% and ~8% between z~2.25 and z~1.25. This is significantly less than the ~37% and ~47% size increases found when using the half-light radius.