A total of 96 absolute gravity (AG) measurements at the Membach station and 221 at the Proudman Oceanographic Laboratory (POL) is analyzed for noise content. The lengths of the series were around 10 years (POL) and 8 years (Membach). First the noise at frequencies lower than 1 cpd is studied. This noise consists in setup-dependent offsets and geophysical colored sources. The setup white noise is estimated using continuous relative superconducting gravity (SG) measurements at Membach. The colored environmental noise affecting both AG and SG is estimated using the maximum likelihood estimation technique to fit two types of stochastic models to the SG time series, power law noise, and first-order Gauss Markov (FOGM) noise. We estimate the noise amplitudes of a white noise process plus power law model while simultaneously solving for the spectral index and the noise amplitudes of a white noise process plus FOGM noise model is also estimated. The gravity rate of change and the associated uncertainties as a function of the noise structure are then computed. At frequencies higher than 1 cpd, a time-varying white noise component usually dominates AG time series. Finally, the POL and Membach experiments are applied to estimate the uncertainties for AG campaigns repeated once or twice a year to monitor crustal deformation. Such repeated AG measurements should allow one to constrain gravity rate of change with an uncertainty of 1 nm s-2 yr-1 (or 0.5 mm yr-1) after 14 or 24 years, depending on the noise model. Therefore long-term measurements using absolute gravimeters are appropriate for monitoring slow vertical tectonic deformation.