A method comprising: providing a drilling fluid that comprises: an invert emulsion, the invert emulsion comprising an oleaginous fluid continuous phase, an aqueous fluid internal phase, and a surfactant; a weighting agent; and a plurality of colloidal particles; wherein 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; and placing the drilling fluid in a subterranean formation via a wellbore penetrating the subterranean formation, wherein the plurality of colloidal particles comprises a fibrous material and at least one type of colloidal particle selected from the group consisting of a ground mineral, a zeolite particle, a sepiolite particle, an attapulgite particle, an illite particle, a montmorillonite particle, a non-organophilic clay particle, a bentonite particle, a quartz particle, a calcium carbonate particle, a silica flour particle, a calcium hydroxide particle, a magnesium hydroxide particle, an alumoxane particle, a carbon nanotube, a fullerene, graphite, a graphene, graphite oxide, a metal nanoparticle, a metal nanorod, a metal nanosphere, a metal nanoplatelet, a non-metal nanoparticle, a non-metal nanorod, a non-metal nanosphere, a non-metal nanoplatelet, a metal oxide nanoparticle, a metal oxide nanorod, a metal oxide nanosphere, a metal oxide nanoplatelet, a hollow microsphere, a hollow nanosphere, a glass sphere, and combinations thereof. providing a drilling fluid that comprises: an invert emulsion, the invert emulsion comprising an oleaginous fluid continuous phase, an aqueous fluid internal phase, and a surfactant; a weighting agent; and a plurality of colloidal particles; wherein 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; and placing the drilling fluid in a subterranean formation via a wellbore penetrating the subterranean formation, wherein the plurality of colloidal particles comprises a fibrous material and at least one type of colloidal particle selected from the group consisting of a ground mineral, a zeolite particle, a sepiolite particle, an attapulgite particle, an illite particle, a montmorillonite particle, a non-organophilic clay particle, a bentonite particle, a quartz particle, a calcium carbonate particle, a silica flour particle, a calcium hydroxide particle, a magnesium hydroxide particle, an alumoxane particle, a carbon nanotube, a fullerene, graphite, a graphene, graphite oxide, a metal nanoparticle, a metal nanorod, a metal nanosphere, a metal nanoplatelet, a non-metal nanoparticle, a non-metal nanorod, a non-metal nanosphere, a non-metal nanoplatelet, a metal oxide nanoparticle, a metal oxide nanorod, a metal oxide nanosphere, a metal oxide nanoplatelet, a hollow microsphere, a hollow nanosphere, a glass sphere, and combinations thereof. an invert emulsion, the invert emulsion comprising an oleaginous fluid continuous phase, an aqueous fluid internal phase, and a surfactant; a weighting agent; and a plurality of colloidal particles; wherein 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; and placing the drilling fluid in a subterranean formation via a wellbore penetrating the subterranean formation, wherein the plurality of colloidal particles comprises a fibrous material and at least one type of colloidal particle selected from the group consisting of a ground mineral, a zeolite particle, a sepiolite particle, an attapulgite particle, an illite particle, a montmorillonite particle, a non-organophilic clay particle, a bentonite particle, a quartz particle, a calcium carbonate particle, a silica flour particle, a calcium hydroxide particle, a magnesium hydroxide particle, an alumoxane particle, a carbon nanotube, a fullerene, graphite, a graphene, graphite oxide, a metal nanoparticle, a metal nanorod, a metal nanosphere, a metal nanoplatelet, a non-metal nanoparticle, a non-metal nanorod, a non-metal nanosphere, a non-metal nanoplatelet, a metal oxide nanoparticle, a metal oxide nanorod, a metal oxide nanosphere, a metal oxide nanoplatelet, a hollow microsphere, a hollow nanosphere, a glass sphere, and combinations thereof.