add_filter('woocommerce_package_rates', 'adjust_shipping_cost_based_on_weight', 10, 2);
function adjust_shipping_cost_based_on_weight($rates, $package) {
    $weight = WC()->cart->get_cart_contents_weight();
    if ($weight > 10) { // Change 10 to your desired weight limit
        foreach ($rates as $rate_key => $rate) {
            if ('flat_rate' === $rate->method_id) {
                $rates[$rate_key]->cost += 10; // Increase cost by $10 for heavy items
            }
        }
    }
    return $rates;
}