Edge covering problem

Let us given a weighted graph:

         3
    A ------- B
    | \     / |
    | 3\  2/  |
    |   \ /   |
   4|    C    |3
    |   / \   |
    | 8/  2\  |
    | /     \ |
    D ------- E
         2

We seek the edgesets to cover the graph, 
that the weights in an edgeset is limited 
and the cost of an edgeset is the number of 
nodes it covers.