I think that it's actually a but in HikaShop where the weight and dimensions of the main product is not transmitted to the variants of the product. That has been fixed on our end and will be in next version of HikaShop. If you add them to the variants, that should work fine. Here is the method:
Go to the Product
Click on Manage Variant - Under Characteristics
Click on a Variant/Characteristics
Input the weight for the Characteristics and save
If it indeed comes from that, you can replace the file administrator/components/com_hikashop/classes/cart.php with the one in the archive below and that should fix the problem