The extensive air showers created by highly energetic cosmic rays are measured at the Pierre Auger Observatory. The development of these air showers in the dynamic medium of the Earth's atmosphere affects the reconstruction and ultimately the determination of the energy for the primary particle. We present an analysis using data from the two surface detector arrays (with 750\,m and 1500\,m spacing) which studies the modulation of the reconstructed energy estimator due to changes in atmospheric pressure and density. These dependencies on local weather are expected to affect the cosmic ray energy measurements by ${\sim}0.5\%$ on average. While this is a rather small effect, not accounting for weather effects can introduce biases in event rates over a sidereal day and must be corrected to perform cleaner anisotropy analyses, in particular at large angular scales. Finally, a method by which these modulations can be corrected is detailed for the 750 m and 1500 m arrays.