Diapirism is crucial for heat and mass transfer in many geodynamic processes. Understanding diapir ascent velocity is vital for assessing its significance in various geodynamic settings. Although analytical estimates exist for ascent velocities of diapirs in power-law viscous, stress weakening fluids, they lack validation through 3D numerical calculations. Here, we improve these estimates by incorporating combined linear and power-law viscous flow and validate them using 3D numerical calculations. We focus on a weak, buoyant sphere in a stress weakening fluid subjected to far-field horizontal simple shear. The ascent velocity depends on two stress ratios: (1) the ratio of buoyancy stress to characteristic stress, controlling the transition from linear to power-law viscous flow, and (2) the ratio of regional stress associated with far-field shearing to characteristic stress. Comparing analytical estimates with numerical calculations, we find analytical estimates are accurate within a factor of two. However, discrepancies arise due to the analytical assumption that deviatoric stresses around the diapir are comparable to buoyancy stresses. Numerical results reveal significantly smaller deviatoric stresses. As deviatoric stresses govern stress-dependent, power-law, viscosity analytical estimates tend to overestimate stress weakening. We introduce a shape factor to improve accuracy. Additionally, we determine characteristic stresses for representative mantle and lower crustal flow laws and discuss practical implications in natural diapirism, such as sediment diapirs in subduction zones, magmatic plutons or exhumation of ultra-high-pressure rocks. Our study enhances understanding of diapir ascent velocities and associated stress conditions, contributing to a thorough comprehension of diapiric processes in geology.