That depends on the amount and if the shipping cost is on the package. I print shipping labels but don't have the cost on the label. If the postage shows the cost you may want to refund. If it is more than a few dollars I refund the overcharge regardless of weather or not the cost was posted on the label. In the end it is up to you as to refunding the overcharge. If the buyer knows the true cost even if it is small it may cause you a problem.
The first place I went to wanted to charge more for shipping it, and I don't think buyer would pay more. So I went to a different place. That ended up being a bit cheaper than what I charged, so I did go out of my way to find cheapest carrier. I feel like I shouldn't need to since I went out of my way. I know that if I had gone with the first carrier, I would not get more money for shipping.
Shipping is is not a way to make a profit. It should be charged by way of calculated shipping as close to the actual cost as possible. You don't go out of your way, you set your listing to charge the real cost as close as you can. If you have other questions about shipping costs you need to ask about how to do it properly