Add this code to your functions.php file. This code will add the backstretch functionality to your theme which handles the loading and sizing of the images.

entry-background.php

<?php
//* Do NOT include the opening php tag

//* Enqueue scripts and styles
add_action( 'wp_enqueue_scripts', 'cegg_load_scripts_styles' );
function cegg_load_scripts_styles() {

	if ( is_singular( array( 'post', 'page' ) ) && has_post_thumbnail() ) {

		wp_enqueue_script( 'cegg-backstretch', get_bloginfo( 'stylesheet_directory' ) . '/js/backstretch.js', array( 'jquery' ), '1.0.0', true );
		wp_enqueue_script( 'cegg-backstretch-set', get_bloginfo( 'stylesheet_directory' ) . '/js/backstretch-set.js' , array( 'jquery', 'cegg-backstretch' ), '1.0.0', true );
	
	}
}

//* Localize backstretch script
add_action( 'genesis_after_entry', 'cegg_set_background_image' );
function cegg_set_background_image() {

	$image = array( 'src' => has_post_thumbnail() ? genesis_get_image( array( 'format' => 'url' ) ) : '' );

	wp_localize_script( 'cegg-backstretch-set', 'BackStretchImg', $image );

}

//* Hook entry background area
add_action( 'genesis_after_header', 'cegg_entry_background' );
function cegg_entry_background() {

	if ( is_singular( 'post' ) || ( is_singular( 'page' ) && has_post_thumbnail() ) ) {

		echo '<div class="entry-background"></div>';
	
	}

}