Show number of articles in menu

I think it would be useful to create a custom walker for your menu. In the following code example I made use of the Menu Item Object. You can take a look at the object output here.

An object type is specified for every menu item. So I just compare if the object is a category. If yes I made use of the specified object ID to get the category + category count. Last but not least I just wrap the category count with a span at the end of the link. I hope it works for you.

Here the code example:

class Menu_Category_Count extends Walker_Nav_Menu {

    var $number = 1;

    function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 ) {
        $indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';

        $class_names = $value="";

        $classes = empty( $item->classes ) ? array() : (array) $item->classes;
        $classes[] = 'menu-item-' . $item->ID;

        $class_names = join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item, $args ) );
        $class_names = $class_names ? ' class="' . esc_attr( $class_names ) . '"' : '';

        $id = apply_filters( 'nav_menu_item_id', 'menu-item-'. $item->ID, $item, $args );
        $id = $id ? ' id="' . esc_attr( $id ) . '"' : '';

        $output .= $indent . '<li' . $id . $value . $class_names .'>';

        $atts = array();
        $atts['title']  = ! empty( $item->attr_title ) ? $item->attr_title : '';
        $atts['target'] = ! empty( $item->target )     ? $item->target     : '';
        $atts['rel']    = ! empty( $item->xfn )        ? $item->xfn        : '';
        $atts['href']   = ! empty( $item->url )        ? $item->url        : '';

        $atts = apply_filters( 'nav_menu_link_attributes', $atts, $item, $args );

        $attributes="";
        foreach ( $atts as $attr => $value ) {
            if ( ! empty( $value ) ) {
                $value = ( 'href' === $attr ) ? esc_url( $value ) : esc_attr( $value );
                $attributes .= ' ' . $attr . '="' . $value . '"';
            }
        }

        // Get Category + Category Count
        $category_count = "";
        if ($item->object == "category") {
            $category = get_category($item->object_id);
            $category_count = $category->category_count;
        }

        $item_output = $args->before;
        $item_output .= '<a'. $attributes .'>';
        $item_output .= $args->link_before . apply_filters( 'the_title', $item->title, $item->ID ) . $args->link_after;
        $item_output .= ($item->object == "category") ? '<span class="count">'.$category_count.'</span>': '';
        $item_output .= '</a>';
        $item_output .= $args->after;

        $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
    }

}

Than just call the custom nav walker where you get your nav menu like this:

wp_nav_menu(
    array(
        ....,
        "walker"            => new Menu_Category_Count(),
    )
);

If you never dealed with a custom nav walker take a look at this tutorial at tutsplus