Lots of ecommerce stores will do the calculation for you based on real rates from the major shippers in the United States.
I used to write such shopping carts, and we did exactly like you are asking, take the individual weights, times the number of items, packed into X number of boxes and sent that information to UPS, FedEx, USPS and for a while DHL and Canada Post. They then used the store owner's account number to return a set of rates based on the shipping services available (for example, you can't ship ground to Hawaii from California)
If you don't have real time shipping available in your shopping cart, estimate the cost from where you are to as far away as you might ship as your max, then take a bit off. You make money on things that are close to you and lose money on things far away, and hopefully it comes out in the wash.
Finally, as a method of selling, incorporate the shipping cost into the price of your item and offer Free Shipping as a way to increase traffic to your site. It seems to be a popular technique.