When LW creates listings in channels with the product weight, the channel doesn't know all the packaging weights - we could compensate for that if we were given the chance to use extended properties to send 'override' shipping weights to channels at our discretion.

With BigCommerce specifically, I would have to spend $50/mo for a shipping 'tool' on the BC side to customize the shipping charges. What is happening is if Linnworks provides the weights, and BC charges the customer based on product weight, we are being shorted on the shipping charges because BC doesn't know the default package weights to be added to the shipping charge.

Yes, Linnworks needs to update controlling the weight. Some products get repackaged and altered over time with no need to create a new product in Linnworks, but once Linnlive pushes a product you can no longer update to a new weight. It's a simple change that needs addressing.