There are many possible answers to your question. You can technically 'weight' a graph by any metric that you want. However, if you are starting with an unweighted network, then it would be difficult to weight it by, e.g., correlation coefficient, due to the fact that that information would be already lost.

My only recommendation is for you to continue searching for datasets online, and / or try to obtain the original data for the networks that you have already accumulated (by having the original data, you could then re-create the networks, but having their weights included this time).

Kevin

There are many ways to create weights, based on some assumptions and interpretations of the data that you have access to.

You may want simply to add -1 and +1 weights to edges to represent positive and negative correlation based on the measurements from Pearson or Spearman correlation being positive or negative. Or you could prefer a real number from the Mutual Information estimation that represents the strength of statistical association between these two nodes in the graph (couple TF-gene). You could also weigh the edge based on the frequency of this edge from all possible graphs. that fit the data distribution that you have. As you can see, there are numerous ways of doing this.