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We study the growth of weighted networks with exponential aging of sites. Each new vertex of the network is connected to some old vertices with proportional (i) to the strength of the old vertex and (ii) to e-ατ, where τ is the age of the old vertex and α is a positive constant. As soon as the preferential attachment is moditied by such factors, the interesting quantities of the produced network (the vertex degree, vertex strength, clustering coefficient and average path length) will be significantly transformed.