The best approach is to implement this as a custom shipping carrier.

You should not read the destination country directly from the request or session. Get the current cart and retrieve the country from the cart's shipping address:

use Webkul\Checkout\Facades\Cart;

$cart = Cart::getCart();

$country = $cart->shipping_address?->country
    ?? $cart->billing_address?->country;

The country value will be the ISO country code, for example:

US
GB
NL
AU

For weight, if you are using Bagisto's native weight attribute, you should use the cart item total_weight instead of recalculating the product weight manually:

$totalWeight = 0;

foreach ($cart->items as $item) {
    if (! $item->getTypeInstance()->isStockable()) {
        continue;
    }

    $totalWeight += (float) $item->total_weight;
}

Using $cart->items is important because all_items may include child items and can result in double-counting for configurable or bundle products.

Then create a custom carrier extending AbstractShipping and perform the country + weight calculation inside the calculate() method:

class InternationalRate extends AbstractShipping
{
    protected $code = 'international';

    public function calculate()
    {
        if (! $this->isAvailable()) {
            return false;
        }

        $cart = Cart::getCart();

        if (! $cart || ! $cart->haveStockableItems()) {
            return false;
        }

        $country = $cart->shipping_address?->country
            ?? $cart->billing_address?->country;

        $weight = 0;

        foreach ($cart->items as $item) {
            if (! $item->getTypeInstance()->isStockable()) {
                continue;
            }

            $weight += (float) $item->total_weight;
        }

        $rates = [
            'US' => ['handling' => 8, 'per_kg' => 2.5],
            'GB' => ['handling' => 6, 'per_kg' => 2],
            'NL' => ['handling' => 6.5, 'per_kg' => 2.2],
            'AU' => ['handling' => 12, 'per_kg' => 4],
        ];

        if (! isset($rates[$country])) {
            return false;
        }

        $basePrice = $rates[$country]['handling']
            + ($weight * $rates[$country]['per_kg']);

        return $this->getRate($basePrice);
    }
}

The main point is:

Cart → Shipping Address Country + Cart Item Weight → Custom Carrier → Calculated Shipping Rate

Also, make sure to set both base_price and price on the CartShippingRate. The base price should be calculated in the store's base currency, while price should be converted using:

$rate->base_price = $basePrice;
$rate->price = core()->convertPrice($basePrice);

If the shipping rules become more complex, such as multiple weight slabs per country, I would recommend storing the rules in a database table rather than hardcoding them.

One important note: if your product weight is stored in a completely custom attribute instead of Bagisto's native weight attribute, total_weight may not be populated. In that case, either map your value to Bagisto's native weight field or calculate it from your custom attribute manually.

For this requirement, a custom shipping carrier is the cleanest and most maintainable Bagisto solution.

Best regards,
Shivendra Gupta
Team Bagisto