I have recently migrated from the Quick Shopping Cart to the Webstore, both due to Intuit shutting down their merchant service and QSC not really being supported and soon to be end of life, as per Go Daddy.
I have a carry over issue from QSC and a new issue with the Webstore. The algorithm used to calculate shipping charges has no provision that allows you to input shipping container sizes and weight. So the only way to add the weight of your shipping materials into the calculation is my adding weight to each product to compensate. This is fine until a customer orders multiple pieces of a given product and suddenly they are now being over charged for shipping. I get complaints about this on a regular basis and have actually lost customers over this. This has been an issue with QSC since at least 2009.
This issue has carried over to the webstore and is compounded by the fact you cannot add a handling charge in the webstore shipping options. In the past I've been able to add a handling charge which helped offset the container weight issue. At least the amount my customers were overcharged was somewhat reduced via the handling charge. This is no longer possible. There is simply no way to add a flat fee in the shipping options.
This is should be fairly trivial to implement since you already have to supply the dimensions and weight of each of your products. So this much volume of product fits in this volume of container, so weight of product plus weight of container times shipping per ounce equals the total charge for shipping.
As for the handling charge, this is a common fee and the webstore product manager should have been all over this long before now. My conversations with Tech Support indicate this is a known issue with the product.
I've been considering move to another vendor for some time but now this is adding to my bottom line costs and increasing customer dissatisfaction. Balls in your court Go Daddy.
I suggest you to move to WordPress CMS. It has a lot of option you can do in eCommerce. If you need any support I will also provide you. You can contact me on firstname.lastname@example.org.