The problem is not your footer expanding, it is related to image dimensions and body.
When you resize your browser (smaller), the background-images' size adapts to the viewport's width, not its height. That means that at a certain point, the image doesn't vertically fit the viewport anymore.
Then what is visible is the background-color of your body.custom-background, which is, coincidentally, exactly the same color as your footer's background (background-color: #cccccc;).
You can change the background-color of your body to distinguish it from the footer. You cannot resize the image to full-browser width AND height simultaneously without distortions.
Sticky footers: I noticed your footer & its wrapper are not positioned fixed or relative, which is the common approach for sticky footers. Then position it with the bottom property.
Fixed position:
- will stick to bottom
- will not scroll
- will always be visible
Relative position:
- will stick to bottom
- will scroll
- will only be visible on reaching page bottom