  Different weighted scale-free networks show weights-topology correlations
indicated by the non linear scaling of the node strength with node
connectivity. In this paper we show that networks with and without
weight-topology correlations can emerge from the same simple growth dynamics of
the node connectivities and of the link weights. A weighted fitness network is
introduced in which both nodes and links are assigned intrinsic fitness. This
model can show a local dependence of the weight-topology correlations and can
undergo a phase transition to a state in which the network is dominated by few
links which acquire a finite fraction of the total weight of the network.
