Nanopapers formed by stiff and strong native cellulose nanofibrils are emerging as mechanically robust and sustainable materials to replace high-performance plastics or as flexible, transparent and "green" substrates for organic electronics. The mechanical properties endowed by nanofibrils crucially depend on mastering structure formation processes and on understanding interfibrillar interactions as well as deformation mechanisms in bulk. Herein, we show how different dispersion states of cellulose nanofibrils, that is, unlike tendencies to interfibrillar aggregation, and different relative humidities influence the mechanical properties of nanopapers. The materials undergo a humidity-induced transition from a predominantly linear elastic behavior in dry state to films displaying plastic deformation due to disengagement of the hydrogen-bonded network and lower nanofibrillar friction at high humidity. A concurrent loss of stiffness and tensile strength of 1 order of magnitude is observed, while maximum elongation stays near constant. Scanning electron microscopy imaging in plastic failure demonstrates pull-out of individual nanofibrils and bundles of nanofibrils, as well as larger mesoscopic layers, stemming from structures organized on different length scales. Moreover, multiple yielding phenomena and substantially increased elongation in strongly disengaged networks, swollen in water, show that strain at break in such nanofibril-based materials is coupled to relaxation of structural entities, such as cooperative entanglements and aggregates, which depend on the pathway of material preparation. The results demonstrate the importance of controlling the state of dispersion and aggregation of nanofibrils by mediating their interactions, and highlight the complexity associated with understanding hierarchically structured nanofibrillar networks under deformation.