Weights for unbalanced classification
Depending on your choice of accuracy metric, you'll find that different balancing ratios give the optimum value of the metric. To see why this is true, consider optimizing precision alone vs. optimizing recall alone. Precision is optimized (=1.0) when there are no false positives. Upweighting negative data reduces the positive rate, and therefore the false positive weight. So if you just want to optimize precision, give the positive data zero weight! You'll always predict negative labels and the precision will be ideal. Likewise, for only optimizing recall, give the negative data zero weight - you'll always get the ideal value of recall. These extreme cases are silly for real-world applications, but they do show that your "best" balancing ratio depends on your metric.

As you're probably aware, metrics like AUC and F1 try to compromise between precision and recall. In the absence of prior information, people often try to choose "equal balance" between precision and recall, as implemented in AUC. Since AUC is relatively insensitive to data balance, 1:1 data balancing is generally appropriate. However, in real life you may care more about precision than recall, or vice versa. So, you do need to select your metric in advance, depending on the problem you're solving. Then keep your metric fixed, vary your data balance, and look at your trained model performance on realistic test datasets. Then you can see whether your model is making the optimum predictions, from the point of view of your chosen metric and your real-world dataset.