An absorbent cellulosic sheet having a variable local basis weight. The sheet includes a papermaking-fiber reticulum having a plurality of fiber-enriched pileated regions of a relatively high local basis weight each extending a distance in a cross-machine direction (CD) of the sheet, and a plurality of elongated densified regions that interconnect the plurality of fiber-enriched pileated regions. The elongated densified regions (i) have a relatively low local basis weight, and each extending a distance in a machine direction (MD) of the sheet, and (ii) are arranged in a repeating pattern having leading and trailing edges, such that the elongated densified regions are longitudinally staggered with respect to each other.