Order BY Most Liked And Published Between Previous Week Monday And Next Week Monday

WordPress allows multiple orders with the orderby parameter. https://codex.wordpress.org/Class_Reference/WP_Query#Order_.26_Orderby_Parameters

'meta_key' => '_liked', // You do it well
'orderby'  => array('meta_value_num' => 'DESC', 'date' => 'DESC'),

Here you tell WordPress to sort by “bigger” likes and last publish date.