Cliff Seal

Simply put: this plugin gives the Editor role access to edit “theme options”, which includes:
<ul>
<li>Appearance > Widgets</li>
<li>Appearance > Menus</li>
<li>Appearance > Customize if they are supported by the current theme</li>
<li>Appearance > Background</li>
<li>Appearance > Header</li>
</ul>
Instead of adding this capability by hand on each client site, just install and activate this plugin—it keeps your <code>functions.php</code> file clean, and keeps this type of functionality where it belongs.
The capability is added to the role once (on plugin activation) and removed when the plugin is deactivated.

Editor Theme Options

Allow editors to access theme options in the Appearance menu.

cmborchert

This plugin for WordPress adds a background-size controller to the Background Image section in the WordPress Customizer.
You can access the new controller by going to Appearance > Customize from the Dashboard, and clicking on the Background Image section.
Once you’ve added your custom background image, you can set your background-image size to: 
 – “Cover”: As large as possible; fills entire view, with cropping. 
 – “Contain”: As large as possible, without cropping; fits inside of view. 
 – “100% width”: Width fits view perfectly, height may be smaller or larger than view (equivalent to css ‘100% auto’). 
 – “100% height”: Height fits view perfectly, width may be smaller or larger than view (equivalent to css ‘auto 100%’). 
 – “Inherit”: Sets background size to whatever parent element is set to (html, in this case). 
 – “Custom”: Allows you to put in your own css to be applied in the section called “CSS for background-size (if ‘custom’ selected).”
To learn more about the CSS background-size property, go to:
https://developer.mozilla.org/en-US/docs/Web/CSS/background-size 
or 
http://www.w3schools.com/cssref/css3_pr_background-size.asp
<h3>Notes</h3>
Notes: 
*The plugin works by adding styles to the body.custom-background class. If the default custom-background support has been disrupted, then this plugin will not work.

Add Background-Size to Customizer

Allows you to control the background-size of your main background image from the comfort of the customizer, using predetermined values or custom CSS.

Editor Theme Options vs Add Background-Size to Customizer