The answer from Pankaj Pareek is absolutely correct. This is the checkout flow on Magento for Paypal Express. Note that your question title is misleading, whether you are using Paypal Payments Pro or Paypal Standard is irrelevant - when the user clicks the button from the cart or product page they are using Paypal Express to check out.
Magento's default Paypal Express checkout flow is dire - it actually takes longer to check out this way than a normal checkout as there's a ludicrous review step. You should note that even though you are using 1.6 it has not improved in the intervening 4.5 years despite them being bought by ebay.
Basically it's a backend config option to pass the shipping methods across.

However there is a bug which means its the id that gets shown in Paypal, not the label. It looks awful in Paypal. I stuck a module to fix it up in this answer;
https://magento.stackexchange.com/questions/6945/paypal-express-shipping-methods/#answer-50290
And other than this small problem the communication on shipping between Paypal and Magento works really well. User updates the address and the shipping options update etc.
You can further improve this flow by removing the review stage altogether in Magento. That is a bit harder, there are modules you can buy that help. It all massively improves conversion rates, it is well worth doing.