How can I separate product variables for shipping weight in my inventory?

Hello! I have a very specific question I need help with. I sell Pokémon cards and we have an item with the same sku but one is heavier to ship and one is lighter to ship (it is the same product). We would like the separate variables to be pulled out of the singular stock. How do we accomplish that?

Yes the customer is able to choose which option they would like. We used
the product variants but we want figure out how to pull it from the same
stock the only solution we have been able to find is a 3rd party app
unfortunately