Perfluorinated ionomers, in particular, Nafion, are a critical component in hydrogen fuel cells as the ion conducting binder within the catalyst layer in which it can be confined to thicknesses on the order of 10 nm or less. It is well reported that many physical properties, such as the Young's modulus, are thickness dependent when the film thickness is less than 100 nm. Here we utilize a cantilever bending methodology to quantify the swelling-induced stresses and relevant mechanical properties of Nafion films as a function of film thickness exposed to cyclic humidity. We observe a factor of 5 increase in the Young's modulus in films thinner than 50 nm and show how this increased stiffness translates to reduced swelling or hydration. The swelling stress was found to increase by a factor of 2 for films approximately 40 nm thick. We demonstrate that thermal annealing enhances the modulus at all film thicknesses and correlate these mechanical changes to chemical changes in the infrared absorption spectra.