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