This paper presents the equations of capillary hydrostatics for interfaces between viscous isotropic fluids and nematic liquid crystals. The interfacial stress balance equation involves the surface divergence of the surface stress tensor. It is shown that the anisotropic elastic contribution due to weak; anchoring give rise to bending stresses not observed in isotropic fluids. It is shown that surface gradients of the bending stresses are a source of interfacial normal forces even in planar interfaces. Surface gradients in the normal surface stresses due to weak anchoring generate interfacial tangential forces, equivalent to those present in the thermocapillarity, electrocapillarity, and diffusocapillarity of isotropic fluids. Mathematical expressions corresponding to biaxial nematics for anisotropic surface elasticity, surface stress tensor, Marangoni and normal forces are derived, characterized, and used to establish the main interfacial phenomena driven by nematic biaxial ordering.