The duplication and divergence process is ubiquitous in nature and man-made networks. Motivated by the duplication-divergence mechanism which depicts the growth of protein networks, we propose a weighted network model in which topological evolution is coupled with weight dynamics. Large scale numerical results indicate that our model can naturally generate networks with power-law-like distributions of degree, strength and weight.The degree-strength correlation is illustrated as well. These properties are in agreement well with empirical data observed in real-world systems. Furthermore, by altering the retention probability σ, weighted, structured exponential networks are realized.