Drilling fluids for oilfield use consist of complex mixtures of natural and synthetic materials. The viscous properties along with the particle size distribution of the applied weight materials are vital in controlling the stability of the microstructure and density of the drilling fluid. Typical oil-based drilling fluids made for North Sea oilfield drilling application with oil–water ratios (OWRs) of 80/20 and 60/40 are examined with respect to their density stability. The stability was analyzed at both rest and dynamic conditions using flow and viscosity tests, oscillatory sweep tests, creep tests, and time-dependent oscillatory sweep tests using a scientific rheometer with a measuring system applying a grooved bob at atmospheric conditions. The quantities used in ranking the stability of the fluids include the yield stress, flow transition index, mechanical storage stability index, and dynamic sag index. We observed that the drilling fluid sample with OWR = 60/40 showed a more stable dispersion with a stronger structure having higher yield stress and flow transition index values, while the mechanical storage stability index and dynamic sag index recorded lower values. Furthermore, the Herschel–Bulkley parameters for yield stress and consistency index increased in fluid with OWR = 60/40, whereas the flow index values for both fluid samples were similar. The results of this study enable drilling fluid engineers to design realistic oil-based drilling fluids with stable microstructure to mitigate weigh material settling and sag of particles for North Sea drilling operation.