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Hypersoft set is an emerging knowledge of study which is projected to address the limitations of soft set for the entitlement of multi-argument approximate function. This function maps sub-parametric tuples to power set of universe. It emphasizes the partitioning of each attribute into its respective attribute-valued set that is missing in existing soft set-like structures. These features make it a completely new mathematical tool for solving problems dealing with uncertainties. In this study, classical concept of weak structures (Wstructures) is characterized under hypersoft set environment which will provide a conceptual framework for further characterization of respective topological spaces and other spaces of functional analysis. Some of its important properties and results are investigated. Moreover, new notions of hypersoft weak axioms W-τ0, W-τ1 and W-τ2 are discussed with illustrative examples.