Manually weighted taxonomy terms

gistfile1.php

<?php

// Use this plugin https://wordpress.org/plugins/i-order-terms/ which will let you drag/drop to re-order terms

// get_terms() will automatically order the terms

// get_the_terms() needs to be sorted afterwards. Example below.

function object_to_array( $object ) {
	if ( is_array( $object ) OR is_object( $object ) ){
		$result = array(); 
		foreach( $object as $key => $value ){ 
			$result[$key] = object_to_array( $value ); 
		}
		return $result;
	}
	return $object;
}

$terms = get_the_terms( get_the_ID(), 'some_taxonomy' );
if ( $terms && ! is_wp_error( $terms ) ) :

	// Deep convert to array
	$terms = object_to_array( $terms );

	// Order by custom_order tag
	usort( $terms, function($a, $b) {
		return $a['custom_order'] - $b['custom_order'];
	});

	foreach( $terms as $term ) {
		echo $option['name'];
	}
endif;