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Composite indicators (CIs), i.e., combinations of many indicators in a unique synthetizing measure, are useful for disentangling multisector phenomena. Prominent questions concern indicators’ weighting, which implies time-consuming activities and should be properly justified. Landscape fragmentation (LF), the subdivision of habitats in smaller and more isolated patches, has been studied through the composite index of landscape fragmentation (CILF). It was originally proposed by us as an unweighted combination of three LF indicators for the study of the phenomenon in Sardinia, Italy. In this paper, we aim at presenting a weighted release of the CILF and at developing the Hamletian question of whether weighting is worthwhile or not. We focus on the sensitivity of the composite to different algorithms combining three weighting patterns (equalization, extraction by principal component analysis, and expert judgment) and three indicators aggregation rules (weighted average mean, weighted geometric mean, and weighted generalized geometric mean). The exercise provides the reader with meaningful results. Higher sensitivity values signal that the effort of weighting leads to more informative composites. Otherwise, high robustness does not mean that weighting was not worthwhile. Weighting per se can be beneficial for more acceptable and viable decisional processes.