© 2020 American Physical Society. ©2020 American Physical Society. Berry curvature, which arises from the asymmetry in a system, is a paramount physical property that results in interesting phenomena such as valley Hall effect. There have been several experimental observations of valley Hall effect in hBN encapsulated bilayer graphene systems as well as hBN/single-layer graphene heterostructures. Although the intent of encapsulating graphene with hBN is to improve the electronic properties of the graphene, the effect of the hBN layer in breaking the layer symmetry and inducing Berry curvature in these systems is not studied explicitly. In this study, we show that for the commensurate state of the heterostructure, the configuration, as well as the orientation of the hBN layer, has an immense effect on the polarity as well as the magnitude of the Berry curvature in bilayer graphene system as they break the layer symmetry. Also, the polarity and the magnitude of the Berry curvature can further be manipulated with the application of an out-of-plane electric field by tuning the layer asymmetry. Whereas, in hBN/single-layer graphene commensurate systems, the presence of an hBN layer breaks the sublattice symmetry and induces Berry curvature, whose magnitude and polarity depend on the configuration and the orientation of the hBN layer. Moreover, although the magnitude can be further tuned with the application of an out-of-plane electric field, the polarity is rather insensitive to the field as the sublattice asymmetry cannot be reversed with the applied field.