In nanometer scale, the electrical double layers (EDLs) formed by the charged channel walls protrude reasonably into the nanochannel creating weak EDL overlapping which becomes unavoidable for thicker EDLs. The reporting investigation considers a purely electroosmotic flow through a nanochannel with weak EDL overlapping accounting for the impact of the magnetic field along with the influence of Hall current. The total EDL potential and the velocity field have been derived in dimensionless forms, where a Taylor series expansion up to the third order is performed in the electroosmotic body force term. A broad span of significant parameters is accounted for while generating the results, such as the Debye–Hückel parameter, Hartmann number, and Hall parameter. For thicker EDL and weak EDL overlapping, EDL potential tends to non-zero smaller values and the flow velocity deviates from a ‘plug-like’ profile with smaller magnitudes. Thicker EDL and weak EDL overlapping reduces the augmentation effect of Hall current on the flow velocity and volumetric flow rate. Smaller Hall parameter and higher Hartmann number values reduce the volumetric flow rate. The incrementing trend of flow rate sensitivity on the Debye–Hückel parameter with the Hall parameter becomes marginal for the lower Hartmann number. Moreover, the rate of decrement of flow rate with Hartmann number is amplified for lower Hall parameters. The increment of flow rate sensitivity on the Hall parameter is drastic for higher Hartmann numbers and smaller Hall parameters. The flow rate is highly over-predicted by the Hall effect and highly under-predicted by weak EDL overlapping for higher values of the Hartmann number.