How to calculate shipping for cart total weight with slab rate?

I recommend getting in touch with WooCommerce’s support about this via https://woocommerce.com/my-account/contact-support/?if you have any of their paid WooCommerce products or https://www.ads-software.com/support/plugin/woocommerce/?if you do not.

Adding Custom Shipping Calculation via Functions.php

You can add a function in your theme’s functions.php file to calculate the shipping cost based on the weight slabs you’ve provided. This approach will add the shipping fee dynamically based on the total weight of the cart.

// Custom shipping calculation based on weight
function custom_shipping_cost_based_on_weight($cart) {
    // Ensure that the cart has items in it
    if (is_admin() && !defined('DOING_AJAX')) return;

    // Get total cart weight
    $total_weight = $cart->get_cart_contents_weight();
    
    // Initialize shipping cost
    $shipping_cost = 0;

    // Shipping logic based on weight
    if ($total_weight <= 2) {
        // Flat rate for up to 2 kg
        $shipping_cost = 45;
    } elseif ($total_weight <= 5) {
        // Rate for 2-5 kg
        $shipping_cost = 45 + ($total_weight - 2) * 12;
    } else {
        // Rate for above 5 kg
        $shipping_cost = 45 + 3 * 12 + ($total_weight - 5) * 14;
    }

    // Add the calculated shipping cost as a fee
    $cart->add_fee('Shipping Charge', $shipping_cost);
}

// Hook into WooCommerce to apply the custom shipping fee during cart calculation
add_action('woocommerce_cart_calculate_fees', 'custom_shipping_cost_based_on_weight');

Always backup your functions.php file before making changes, and test in a staging environment if possible to avoid any issues on your live site.