Invert emulsion drilling fluids that have extended emulsion stability and reduced sag potential are described herein. The drilling fluids comprise an invert emulsion, a weighting agent, and a plurality of colloidal particles. The invert emulsion comprises an oleaginous fluid continuous phase, an aqueous fluid internal phase, and a surfactant. At least a portion of the plurality of colloidal particles interact with the surfactant to form an associative supporting structure that inhibits sag of the weighting agent. In some embodiments, the weighting agent comprises barite particles, particularly barite particles that are less than about 45 μm in size. Methods for placing the invert emulsion drilling fluids in a subterranean formation via a wellbore are also disclosed.