I have been underpaid for shipping fees (my own fault) but never overcharged, I weight my items before hand, if made to order I gather the materials and weight them and the envelope and the card.
I don't think the client is paying the full shipping like this, because it doesn't pay the time I spend walking to the postal office (yes I walk there and it takes me almost an hour), neither the wrapping. I think the second part of the shipping cost should be included in the item price. Actually price like photos, tags or new products is something we should always be working on.
And none of the clients I undercharged ever paid me more for the rest of the shipping. If you've stated that that was the shipping cost and the person accepted it, unless it's an outrageous difference I see no point in returning the variance.
If you're at a B&M shop and it happens that day they don’t have paper bags so they hand you a cheaper plastic bag, they then don't go and refund you for serving you a different bag.