Most of the transportation networks are not determined by their topology only but also by the traffic taking place on the links. It is therefore crucial to characterize the traffic and its possible correlations with the network’s topology. We first define and introduce some of the tools which allows for the characterization of the traffic and the structure of a weighted network. We illustrate these measures on the example of the airport network in which the nodes are airports and where links represent direct connections. The weight on each link is then given by the number of passengers. The main results are the following: (i) the traffic is very heterogeneous and is distributed according to a broad law; (ii) the number of passengers per connection is not constant and increases with the number of connections of an airport, which implies that traffic and topology are not independent. More generally, these measures show that the traffic cannot in general be ignored and that the modeling of transportation networks has to integrate simultaneously both the topology and the weights. We thus propose a model which allows to explain some of the features observed in real-world networks. The main ingredient in this weighted network growth model is a dynamical coupling between weights and links: every time a new link enters the system, the traffic is perturbed. We show that this simple ingredient allows to understand the structure of some real-world weighted networks as well as the interplay between traffic flows and the network’s architecture.