We demonstrate that superhydrophobic and superoleophobic nanocellulose aerogels, consisting of fibrillar networks and aggregates with structures at different length scales, support considerable load on a water surface and also on oils as inspired by floatation of insects on water due to their superhydrophobic legs. The aerogel is capable of supporting a weight nearly 3 orders of magnitude larger than the weight of the aerogel itself. The load support is achieved by surface tension acting at different length scales: at the macroscopic scale along the perimeter of the carrier, and at the microscopic scale along the cellulose nanofibers by preventing soaking of the aerogel thus ensuring buoyancy. Furthermore, we demonstrate high-adhesive pinning of water and oil droplets, gas permeability, light reflection at the plastron in water and oil, and viscous drag reduction of the fluorinated aerogel in contact with oil. We foresee applications including buoyant, gas permeable, dirt-repellent coatings for miniature sensors and other devices floating on generic liquid surfaces.