We derive changes in ocean bottom pressure (OBP) and ocean mass by combining modeled ocean bottom pressure, weekly GRACE-derived models of gravity change, and large-scale deformation patterns sensed by a global network of GPS stations in a joint least squares inversion. The weekly combination allows a consistent estimation of geocenter motion, loading mass harmonics up to degree 30, and a spatially uniform mass correction term, which serves as a correction for forcing of the ocean model. We provide maps and time series of ocean mass and bottom pressure variations. Furthermore, we discuss the estimated geocenter motion and the estimated model correction. Our results indicate that the total ocean mass change is predominantly annual, with a maximum amplitude corresponding to 7.4 mm in October, which is in line with earlier work. The mean ocean bottom pressure (i.e., ocean plus atmospheric mass) shows an annual amplitude of 8.7 mm and is shifted forward by about 1.5 months. In addition, the solution exhibits typical autocorrelation times of about 2 weeks. A comparison with in situ bottom pressure time series in the southern Indian Ocean shows a good agreement, with correlations of 0.7-0.8. Based on these comparisons, we see that our results monitor realistic submonthly variations, which are strongest at high latitudes. The addition of GRACE data in the inversion is found to improve these high-latitude variations and enables better separability of the geocenter motion from other unknowns. Increasing the OBP model error from 3 cm to 4.8 cm affects mainly the higher-degree coefficients.