Show Total Weight in Admin Orders in WooCommerce

/* Show Weight in Admin Orders */
add_action( 'woocommerce_checkout_update_order_meta', 'save_weight_order' );
function save_weight_order( $order_id ) {
    $weight = WC()->cart->get_cart_contents_weight();
    update_post_meta( $order_id, '_cart_weight', $weight );
}
add_action( 'woocommerce_admin_order_data_after_billing_address', 'delivery_weight_display_admin_order_meta', 10, 1 );
function delivery_weight_display_admin_order_meta( $order ) {    
    echo '<p><strong>Order Weight:</strong> ' . get_post_meta( $order->get_id(), '_cart_weight', true ) . get_option( 'woocommerce_weight_unit' ) . '</p>';
}

Source: Business Bloomer

If you want to know the total weight of the cart your customer has placed an order for, use the above code in your theme’s functions.php.

This code will add an extra entry in the ‘Order Details‘ page of each order. Make sure you add the ‘weight value’ of all products in your shop in their listings (shipping information).

When the customer places the order, the total weight of the cart is displayed. i.e. weight value of all individual items is added. Only the total weight value is shown.