  We consider a weighted random walk on the backbone of an oriented percolation
cluster. We determine necessary conditions on the weights for Brownian scaling
limits under the annealed and the quenched law. This model is a random walk in
dynamic random environment (RWDRE), where the environment is mixing,
non-Markovian and not elliptic. We provide a generalization of results obtained
previously by Birkner et al. (2013).
