Rearrange shipping methods

functions.php

add_filter('woocommerce_package_rates', 'wf_sort_shipping_methods', 10, 2);

function wf_sort_shipping_methods($available_shipping_methods, $package)
{
	// Arrange shipping methods as per your requirement
	$sort_order	= array(
		'wf_shipping_ups'	=>	array(),
		'wf_shipping_usps'	=>	array(),
		'free_shipping'		=>	array(),
		'local_pickup'		=>	array(),
		'legacy_flat_rate'	=>	array(),		
	);
	
	// unsetting all methods that needs to be sorted
	foreach($available_shipping_methods as $carrier_id => $carrier){
		$carrier_name	=	current(explode(":",$carrier_id));
		if(array_key_exists($carrier_name,$sort_order)){
			$sort_order[$carrier_name][$carrier_id]	=		$available_shipping_methods[$carrier_id];
			unset($available_shipping_methods[$carrier_id]);
		}
	}
	
	// adding methods again according to sort order array
	foreach($sort_order as $carriers){
		$available_shipping_methods	=	array_merge($available_shipping_methods,$carriers);
	}
	return $available_shipping_methods;
}