We investigate in this paper various approaches to correct gravity changes for the effect of atmospheric pressure changes. Two specific locations are considered: Strasbourg (France) as mid-latitude station, where regular pressure fronts occur and Djougou (Benin) as equatorial station with large thermally driven S1 and S2 waves of planetary extent. We first review the classical approaches based on a constant or frequency-dependent admittance using only local pressure and gravity data. We consider then a model of atmospheric loading and show the barometric admittance in terms of elastic, Newtonian and total load, as a function of the distance from the station. We consider both a 2D pressure model (surface loading) and a 2.5D model, where the density decreases with height (standard atmosphere). Assuming horizontal advection in the atmospheric dynamics, we convert this spatially dependent admittance into a frequency-dependent admittance. Using global pressure data from European Centre for Medium-Range Weather Forecasts (ECMWF) at about 12 km spatial resolution and 3 h sampling, we compute the model-predicted pressure admittance for Djougou and Strasbourg and we simulate the frequency dependence inferred from gravity and pressure observations below 4 cycle per day. A long gravity and pressure data set (1996-2013) from Strasbourg is used to investigate the low frequency part of the pressure admittance while a common 2.5 year data set (August 2010-February 2013) for Strasbourg and Djougou is then analyzed to investigate the high frequency part of the admittance. In both cases, our results are in close agreement with the predictions inferred from an atmospheric 2.5D loading model with a distance-time relationship due to horizontal advection. The frequency dependence of the barometric admittance is explained by the competing contributions of Newtonian attraction and elastic surface deformation according to the distance from the gravimeter. In the far field (low frequencies), the magnitude of the admittance decreases with frequency because of the combined elasticity effect and Newtonian attraction (when the atmosphere is below the horizon) while, on the contrary, in the near field (high frequencies), elasticity becomes negligible and the pressure admittance mainly decreases with increasing frequency because of the decreasing attraction effect of the atmospheric masses inside the cylindrical pressure cell centered on the sensor location of decreasing radius. In the last part, we show that there is variability in time in the pressure admittance for both stations.