We experimentally probe a granular system at the microscale to obtain particle positions, inter-particle contacts and the associated forces. These data are obtained by using a laser sheet scanning technique, followed by dedicated reconstruction algorithms. We then apply multiple cycles of uniaxial compression and decompression to a collection of hydrogel particles. Although the particles interact via a purely repulsive Hertzian force law, f ~ x3/2, when the particles are pushed together by a distance, x, the global force response, F, to global compression by X grows much faster than X3/2. We show that this response is due to changes in the microstructure. We find that changes in F in response to a macroscale stresss/strain are related to changes in system-wide measures of the microstructure and the inter-grain force, in addition to the increases of the forces at contacts. These data are consistent with a scaling relation that connects the observed microscopic response of the particles to the independently measured macroscopic pressure inside the packing.