  We introduce a model of evolving preferential attachment trees where vertices
are assigned weights, and the evolution of a vertex depends not only on its own
weight, but also on the weights of its neighbours. We study the distribution of
edges with endpoints having certain weights, and the distribution of degrees of
vertices having a given weight. We show that the former exhibits a condensation
phenomenon under a certain critical condition, whereas the latter converges
almost surely to a distribution that resembles a power law distribution.
Moreover, in the absence of condensation, we prove almost-sure setwise
convergence of the related quantities. This generalises existing results on the
Bianconi-Barab\'{a}si tree as well as on an evolving tree model introduced by
the second author.
