Previously, the production of stable high-beta plasmas in the University of Wisconsin Levitated Toroidal Octupole has been reported. The plasma beta measured in the bad-curvature region ranges from β ~ 8% to 44% (ne ≈ (2–5) × 1013 cm−3, Bpol ≈ 200–860 G) in macroscopically stable plasmas with decay times in excess of 1000 Alfvén times. In this paper, theoretical work performed on non-MHD effects to explain the significant enhancement of plasma stability above the ideal-MHD ballooning instability limit of 4% is described. The effects are included in finite-n MHD theory and a detailed kinetic treatment including finite Larmor radius (FLR) and heat flow along field lines. The FLR effects are sufficient to explain the stability of the β = 8% plasma through coupling of the ballooning mode to a stable oscillatory ion drift wave. This cannot explain the stability of the more collisional, larger-gyroradius β = 44% plasma. Equilibrium diamagnetism is strongly affected by ion gyroviscosity in this plasma, and the role of this effect on the equilibrium and stability is discussed.