Understanding various aspects of unconventional ferroelectricity in hafnia-based materials is of major importance for the development of future non-volatile memory and logic devices. Here, we investigate the unconventional and weak electromechanical response of epitaxial La0.67Sr0.33MnO3/Hf0.5Zr0.5O2/La0.67Sr0.33MnO3 ferroelectric capacitors via the sensitivity of nanobeam X-ray diffraction experiments during application of electrical bias. We show that the virgin rhombohedral phase exhibits a negative linear piezoelectric effect with piezoelectric coefficient (d33) ~ 0.5 to 0.8 pm/V. Above the coercive voltage, the piezoelectric coefficient is suppressed. For higher voltages, and with the onset of DC conductivity throughout the capacitor, a second-order effect is observed.