Nuclear pore complexes control the exchange of macromolecules between the cytoplasm and the nucleus. A selective permeability barrier that arises from a supramolecular assembly of intrinsically unfolded nucleoporin domains rich in phenylalanine-glycine dipeptides (FG domains) fills the nuclear pore. There is increasing evidence that selective transport requires cohesive FG domain interactions. To understand the functional roles of cohesive interactions, we studied monolayers of end-grafted FG domains as a bottom-up nanoscale model system of the permeability barrier. Based on detailed physicochemical analysis of the model films and comparison of the data with polymer theory, we propose that cohesiveness is tuned to promote rapid assembly of the permeability barrier and to generate a stable and compact pore-filling meshwork with a small mesh size. Our results highlight the functional importance of weak interactions, typically a few kBT per chain, and contribute important information to understand the mechanism of size-selective transport.