The unique nonlinear dielectric properties of antiferroelectric (AFE) oxides are promising for advancements in solid state supercapacitor, actuator, and memory technologies. AFE behavior in high-k ZrO₂ is of particular technological interest, but the origin of antiferroelectricity in ZrO₂ remains questionable. The theory of reversible electric field-induced phase transitions between the nonpolar P4₂/nmc tetragonal phase and the polar Pca2₁ orthorhombic phase is experimentally tested with local structural and electromechanical characterization of AFE ZrO₂ thin films. Piezoresponse force microscopy identifies signature evidence of a field-induced phase transition. A significant size effect in AFE ZrO₂ is experimentally observed as film thickness is scaled down from 14.7 to 4.3 nm. The size effect is explained by modifications to the phase transition energy barrier heights ranging from 0.6 to 7.6 meV f.u⁻¹ depending on crystallite size and in-plane compressive strain with decreasing ZrO₂ film thickness. Using the size effect, it is possible to double the energy storage density in ZrO₂ from 20 J cm⁻³ to greater than 40 J cm⁻³, thus highlighting a feasible route for superior performance in AFE fluorite supercapacitors.