Trouble saving settings on options page

I’m having trouble saving settings. I think I’ve got everything set up correctly, but when I click “Save Changes,” it says “Settings saved” but doesn’t actually update anything in the database. What am I doing wrong. I feel like it’s something obvious.

By the way, the way I’m doing it is setting up an associative array of setting groups ($setting_groups) with settings in them and looping through it to add and register settings.

Here’s my code:

<?php
var $setting_groups = array(
	'lazyloadxt-general' => array(
			'title' => 'General Settings',
			'settings' => array(
				'lazyloadxt_min' => array('Minimize Scripts','checkbox'),
				'lazyloadxt_extra' => array('Extras','checkbox'),
			)
		),
	);

function __construct() {
	if ( is_admin() ){
		add_action( 'admin_menu', array($this,'admin_menu') );
		add_action( 'admin_init', array($this,'register_settings') );
	}
}
function admin_menu() {
	add_options_page('Lazy Load XT Settings', 'Lazy Load XT', 'administrator','lazyloadxt',array($this,'settings_page'));
}

function register_settings() {
	$setting_groups = $this->setting_groups;
	foreach ($setting_groups as $group => $settings) {
		add_settings_section(
	        $group,         // ID used to identify this section and with which to register options
	        $settings['title'],                  // Title to be displayed on the administration page
	        array($this,'settings_section_callback'), // Callback used to render the description of the section
	        'lazyloadxt'                           // Page on which to add this section of options
	    );
		foreach ($settings['settings'] as $setting => $setting_args) {
			register_setting('lazyloadxt',$setting);
			add_settings_field (
				$setting,
				$setting_args[0],
				array($this,'form_field'),
				'lazyloadxt',
				$group,
				array(
					'id' => $setting,
					'type' => $setting_args[1]
				)
			);
		}
	}
}

function settings_section_callback($args) {
}

function form_field($args) {
	if ($args['type'] == 'checkbox') {
		$val = (get_option($args['id'])) ? 'checked="checked' : '';
		echo '<input type="checkbox" value="1" '.$val.' />';
	}
}

function settings_page() {
    ?>
    <div class="wrap">
        <?php screen_icon(); ?>
        <h2>Lazy Load XT Settings</h2>
        <form method="post" action="options.php">
        <?php
            // This prints out all hidden setting fields
            settings_fields( 'lazyloadxt' );
            do_settings_sections( 'lazyloadxt' );
            submit_button();
        ?>
        </form>
    </div>
    <?php
}