There is on feature that I find lacking in Genesis them and that is not able to change sidebar width from your WordPress interface.
I hope they add this functions in the future versions.
But for that time, you would need to find some other method.
And that method is editing the CSS file of your Genesis child theme.
Understanding Genesis CSS
Outside CSS file, the sidebars are called primary and secondary sidebars, primary sidebar being the one that is displayed when you choose only one sidebar to display.
However in CSS file primary sidebar is merely called sidebar and secondary sidebar is called sidebar-alt.
This is confusing but it is the way they call them in CSS file.
Therefore you need to change the width of sidebar-alt in your CSS file of Genesis child theme.
But that alone would not cause the desired effect. Instead, it would cause the sidebar content to drop down.
Because there is another parameters governing the width of sidebars.
You need to alter the following. You need to reduce the following parameters by the same amount you have increased your sidebar or sidebar-alt, to make allowance.
Note: You can also adjust the sidebars to accommodate each other.