How can i display the posts per week in a particular month?

You’ll need to add a condition to the posts_where filter in wordpress. I have an example here for only pulling posts that are from the current post’s date and earlier:

Add this to functions.php

// filter wp_query when $dated_before is set
function dg_dated_before($where)
{
    global $wp_query, $wpdb, $dated_before;
    if (isset($dated_before)):
        $where = $where . " AND $wpdb->posts.post_date <= '". $dated_before . "' " ;
    endif;
    return $where ;
}
add_filter('posts_where', 'dg_dated_before') ;

Use this, or similar wherever it is that you are running your query:

global $dated_before;
$dated_before = $post->post_date;
$queryObject = new WP_Query();

You’ll obviously need to modify this to add the date boundaries that you need.