Graphene holds great promise in the field of nanoelectronic devices owing to its high carrier mobility, excellent electrical properties, and robust mechanical performance. Theoretically, the Dirac cone band structure of intrinsic graphene endows it with unique electronic characteristics. However, the practical utility of standalone graphene layers is limited by challenges such as insufficient mechanical self-support and high environmental sensitivity. In recent years, hexagonal boron nitride (h-BN), a two-dimensional material structurally analogous to graphene, has emerged as an ideal candidate for constructing van der Waals heterostructures. These heterostructures not only provide mechanical support and environmental protection for graphene, but also modulate its band structure and electronic transport properties, thereby broadening its technological applicability. This paper investigates three distinct stacking configurations of graphene/hexagonal boron nitride (h-BN) heterostructures, focusing on their structural, electronic, and piezoresistive properties. The three configurations along the c-axis are defined as follows: carbon atoms aligned with both nitrogen and boron atoms (G-BN1), nitrogen atoms centered within the carbon hexagonal rings (G-BN2), and boron atoms centered within the carbon hexagonal rings (G-BN3). Structural optimization of these heterostructures is performed using density functional theory (DFT) with the generalized gradient approximation (GGA). Interlayer binding energy calculations reveal that G-BN2 exhibits the lowest binding energy, indicating relatively stronger interlayer interactions between graphene and h-BN in this configuration. The band structures and density of states (DOS) for all three stacking arrangements are computed using the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional. The results demonstrate that h-BN induces a bandgap in graphene by modulating its π-electron band structure. In-plane uniaxial and biaxial tensile strains induced by external stress are simulated by increasing the lattice constants along the a-axis and along both the a- and b-axes, respectively. The band structure variations and piezoresistive properties of the three stacking configurations under these strain conditions are calculated. Compared with the unstrained structures, the bandgaps of all heterostructures significantly increase under uniaxial strain but narrow under biaxial strain. Furthermore, graphene/h-BN heterostructures substantially enhance the piezoresistive coefficient of graphene, with the anisotropic response of electronic orbitals yielding higher piezoresistive coefficients under uniaxial strain across all configurations. Among them, the G-BN2 stacking configuration exhibits the highest piezoresistive coefficient under both strain conditions. This study provides a theoretical foundation for the future design of high-performance graphene-based piezoresistive devices.