Couple of thoughts:
Background images can NOT be made responsive. Sadly. They're fixed. Really irritating but that's the way it is. It's not a theme thing, it's a CSS/HTML thing. The only way around it is to absolutely position your div containing text etc. above a standard image and give them both percentage widths.
The Childishly Simple theme has an option to turn on custom background (scroll down to 'Body background color'.) The background image will then fill the full width of the screen (don't know if that's what you were looking for) PROVIDED that the image is at least the width of the screen e.g. somewhere around 1200px wide