Hi,
First, please note that when you first install HikaShop and go through the installation wizard, it will ask you whether you're going to sell virtual goods, or shippable goods or both.
If you select that you'll sell only shippable goods, then the "force shipping regardless of weight" setting will be turned on so shipping will be required even if the product has no weight.
Also, with next version of HikaShop, the weight of the order will be stored along with the order when created and displayed in the backend when editing the order. So it should be easier to understand that there is a problem with the weight of the products in these orders.
Now displaying the weight of the products in the backend listing could be interesting. However, each information added to that listing requires an extra column. And it might not be used by most people. Someone else might want another column, like the brand, or the retail price, or something else. And custom product fields can also take a lot of space.
At the same time, the width of the products listing is quite limited.
Note also that if you had reproduced the issue by adding the same products in the cart, you would have seen that shipping methods wouldn't appear in the checkout. And we have a FAQ about this here:
www.hikashop.com/support/documentation/106-faq.html#ship
Among the causes pointed out, you'll find:
5) Check that your products have a weight, otherwise, the system won't display any shipping methods as it will consider the products as virtual goods.
So I believe you ended up in a "worst case scenario", and the improvement to the orders manager with the weight display in the next version should already help avoid having to spend a day figuring out the issue.