How could I go about finding the weights or importance of inputs based on outputs?
Pearson correlation can be used for this purpose. The Pearson correlation between two entity shows that how mush the values of these two are  linearly related to each other. 


  According to the Cauchy–Schwarz inequality it has a value between +1
  and −1, where 1 is total positive linear correlation, 0 is no linear
  correlation, and −1 is total negative linear correlation.


According to the values you reported here, there is a strong correlation between doc and mrr so the role of doc in the prediction of mrr is more important than others. 

But on the other hand none of the features doesn't have any considerable linear correlation with ra. In this case you can test some other correlation methods.

For further information visit here. It can be helpful to you. 

Conclusion: the most important feature in predicting an output is the most correlated one with it which has a considerable correlation.