At the breakpoint you want them to sit side by side, try the following:
// This will tell the sidebar to be full-width rather than the set 300px
aside#sidebar {
width:100%;
}
.widget {
// This sets the max-width of the ad area to 50%
max-width: 50%;
// This tells the browser to put the border and any padding inside the max-width
box-sizing: border-box;
// This will sit the elements next to each other
float: left;
}
.textwidget {
// This overrides the 300px width on the inner div
width: auto;
}