If you are uploading images the same size as the large size in your WordPress installation, then set your Large size to 0x0 in Settings -> Media or remove this line:
add_image_size( 'large-size', $LARGE_SIZE, 9999 );
EDIT #1:
Try to add this filter to delete the original image:
add_filter('wp_generate_attachment_metadata', 'delete_fullsize_image');
function delete_fullsize_image($metadata) {
$upload_dir = wp_upload_dir();
$full_image_path = trailingslashit($upload_dir['basedir']) . $metadata['file'];
$deleted = unlink($full_image_path);
return $metadata;
}
It will delete the original image after upload and keep only the generated ones.
EDIT #2:
Check these two plugins (untested), they might help you do it automatically: