  Weighted Lie algebroids were recently introduced as Lie algebroids equipped
with an additional compatible non-negative grading, and represent a wide
generalisation of the notion of a VB -algebroid. There is a close relation
between two term representations up to homotopy of Lie algebroids and VB -
algebroids. In this paper we show how this relation generalises to weighted Lie
algebroids and in doing so we uncover new and natural examples of higher term
representations up to homotopy of Lie algebroids. Moreover, we show how the van
Est theorem generalises to weighted objects.
