  Motivated by properties of higher tangent lifts of geometric structures, we
introduce concepts of weighted structures for various geometric objects on a
manifold F equipped with a homogeneity structure. The latter is a smooth action
on F of the monoid of multiplicative reals. Vector bundles are particular cases
of homogeneity structures with the action being the multiplication of vectors
by reals, and weighted structures on them we call VB-structures. In the case of
Lie algebroids and Lie groupoids, the weighted structures include the concepts
of VB-algebroids and VB-groupoids, intensively studied recently in the
literature. Investigating various weighted structures, we prove some
interesting results about their properties.
