The frequency and properties of multiple star systems offer powerful tests of star formation models. Multiplicity surveys over the past decade have shown that binary properties vary strongly with mass, but the functional forms and the interplay between frequency and semimajor axis remain largely unconstrained. We present the results of a large-scale survey of multiplicity at the bottom of the initial mass function in several nearby young associations, encompassing 78 very low mass members observed with Keck laser guide star adaptive optics. Our survey confirms the overall trend observed in the field for lower-mass binary systems to be less frequent and more compact, including a null detection for any substellar binary systems with separations wider than ~7AU. Combined with a Bayesian re-analysis of existing surveys, our results demonstrate that the binary frequency and binary separations decline smoothly between masses of 0.5M_{sun}_ and 0.02M_{sun}_, though we cannot distinguish the functional form of this decline due to a degeneracy between the total binary frequency and the mean binary separation. We also show that the mass ratio distribution becomes progressively more concentrated at q~1 for declining masses, though a small number of systems appear to have unusually wide separations and low-mass ratios for their mass. Finally, we compare our results to synthetic binary populations generated by smoothed particle hydrodynamic simulations, noting the similarities and discussing possible explanations for the differences.