An absorbent cellulosic sheet having a variable local basis weight. The sheet includes a papermaking-fiber reticulum having (a) a plurality of fiber-enriched pileated regions of a relatively high local basis weight each extending a distance in the cross-machine direction (CD) of the sheet, and (b) a plurality of elongated densified regions of compressed papermaking fibers that interconnect the plurality of fiber-enriched pileated regions. The elongated densified regions (i) have a relatively low local basis weight and each extend a distance in the machine direction (MD) of the sheet, (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, and (iii) have MD/CD aspect ratios of at least 1.5.