Nucleoporins (nups) in the central channel of nuclear pore complexes (NPCs) form a selective barrier that suppresses the diffusion of most macromolecules while enabling rapid transport of nuclear transport receptors (NTRs) with bound cargos. The complex molecular interactions between nups and NTRs have been thought to underlie the gatekeeping function of the NPC. Recent studies have shown considerable variation in NPC diameter but how altering NPC diameter might impact the selective barrier properties remains unclear. Here, we build DNA nanopores with programmable diameters and nup arrangement to mimic NPCs of different diameters. We use hepatitis B virus (HBV) capsids as a model for large-size cargos. We find that Nup62 proteins form a dynamic cross-channel meshwork impermeable to HBV capsids when grafted on the interior of 60-nm wide nanopores but not in 79-nm pores, where Nup62 cluster locally. Furthermore, importing substantially changes the dynamics of Nup62 assemblies and facilitates the passage of HBV capsids through NPC mimics containing Nup62 and Nup153. Our study shows the transport channel width is critical to the permeability of nup barriers and underscores the role of NTRs in dynamically remodeling nup assemblies and mediating the nuclear entry of viruses.