Ok…let’s start.
The widgets are all inside a div with id of sidebar
which has a background color of white so that is the color that IS showing through.
Assuming you mean that you want the light blue to show through, I would just change that white to transparent.
I can’t find a specific line for this in a linked stylesheet so I am guessing its built into the theme somehow.
If you add a new line into your stylesheet it might override this setting.
Then on line 1179 of the stylesheet do this:
#sidebar .widget,
#sidebar-alt .widget {
clear: both;
overflow: hidden;
padding-bottom: 50px;
background-color: transparent; <---remove this
margin-top: 20px;
background-color: white; <--- add this
}
You may have to tweak a bit but that should get you started.