How to mark nodes and insert weights in an adjacency graph?

I have a graph with 12 nodes. The x and y coordinates are give as

xcord={154.780094065851,    302.747331652902,   348.235746943268,   959.228504576796,   1021.26721027296,   1114.13365936238,   358.208241883160,   181.741156296042,   838.759299985938,   906.502702816486,   662.579285251179,   536.372745335719};  ycord={347.543166449207,    461.536311618993,   261.753095520236,   431.778284592051,   250.920713280060,   432.113192132818,   1044.66583584371,   1044.70069210915,   1135.19457237168,   984.121301679063,   792.153882418914,   708.946190878097}; 

Also, these are the edges connecting the nodes.

Edges={{1,2},{1,3},{1,8},{1,11},{1,12},{2,3},{2,4},{2,7},{2,8},{2,11},{2,12},{3,4},{3,5},{3,11},{3,12},{4,5},{4,6},{4,10},{4,11},{4,12},{5,6},{5,11},{5,12},{6,10},{6,11},{6,12},{7,8},{7,9},{7,10},{7,11},{7,12},{8,9},{8,11},{8,12},{9,10},{9,11},{9,12},{10,11},{10,12},{11,12}}; 

Let’s say, The weight of the edges are randomly generated.

I want to plot the graph. The nodes should be depicted as circles with the index within it. I also want to place the weight over the edges.

How can I do it?