I strongly disagree with Elizabeth. Customers have to pay the cost of shipping. $8 is steep, and if I had to pay extra for it I'd be pretty upset, but if I wanted the item enough, I'd pay it. Sometimes shipping costs can make or break a sale.
Personally, however, if I was already at the post office, and could afford it, I'd eat the cost this once and adjust my shipping costs appropriately. But at the same time $8 is such a steep amount to increase by, regardless of who has to pay it.
You're better off contacting the customer and apologising, offering them the opportunity to cancel the order or pay the shipping. Perhaps give them a discount off of any future purchase to make up for it - they may return, even with steep shipping.
Or you could cut a deal, because it's an $8 increase, if you feel that bad you could always pay half and half.