Disclosed are cleaning sheets having at least two regions, where the regions are distinguished by basis weight. In particular, the cleaning sheet comprises one or more high basis weight regions having a basis weight of from about 30 to about 120 g/m2 and one or more low basis weight regions, wherein the low basis weight region(s) have a basis weight that is not more than about 80 % of the basis weight of the high basis weight region(s). Also disclosed are cleaning sheets having substantial macroscopic three-dimensionality, in addition to having multiple basis weights. Optionally, the macroscopically three-dimensional cleaning sheets can comprise a scrim material, which when heated and then cooled, contracts so as to provide a macroscopic three-dimensional structure. Macroscopic three-dimensionality is described in terms of 'average height differential', as well as the 'average peak-to-peak' distance. Processes for using said sheets, benefits of said processes, and articles of manufacture are disclosed.