Two sites are currently being considered as potential locations for the Atacama Large Aperture Telescope (AtLAST) project. The science case has driven the design of the telescope with a dish diameter of 50 metres, but without a protective dome. Monitoring of the meteorological conditions, particularly the magnitude of the wind, is therefore considered very important to support the antenna/telescope design. Hence, our weather stations setup at both sites, operating since late 2022, include high sampling frequency wind anemometers at 12-m and 24-m above the ground level. Air temperature and wind, relevant for the long-term site characterisation, are provided from the ambient conditions monitoring done with sensors in a nearby weather tower owned and operated by the APEX radio telescope project. In this talk we will summarise the results from the study of atmospheric conditions at these potential sites, specifically: the wind power spectra for various conditions of wind, long-term wind speed and air temperature conditions for day and night as well as seasonal conditions. The information is all relevant for the AtLAST antenna design as to achieve the required pointing and tracking performance, but also important to support the science operations of the telescope.