The metallic nature of the low-temperature conductivity σ of the layered manganite La1.2Sr1.8Mn2O7 is not obviously consistent with the very low values of σ nor its slightly semiconducting behavior. We report low-temperature data in an applied field H which exhibit a positive √H correction to σ, for fields perpendicular to the Mn-O bilayers and also parallel to the layers, as well as for both current directions. This behavior is consistent with weak-localization effects in three-dimensional metals and with the theory of quantum interference, recently extended to highly anisotropic layered metals. In addition, a simple model is presented that adequately describes the positive magnetoconductance due to the suppression of spin waves.