Fluid-numerical studies have been carried out to investigate the scaling of the stable magnetic sheath thickness ΔLs with β, Te/Ti, n0, etc., in a collisionless finite-β plasma column. The system is initially close to a two-fluid equilibrium with sheath width ΔL sufficiently narrow for the azimuthal current to trigger various cross-field instabilities (ion acoustic, modified two-stream, Buneman). The enhanced field fluctuations in the sheath region, in addition to heating the plasma locally, leads to a decrease in azimuthal current and a corresponding increase in sheath width to some stable value ΔLs, achieved as the system stabilizes and the field level saturates. The final sheath width in the numerical studies agrees well with the theoretical estimate.