@gnaut There's not a way to display the rates calculated by a shipping extension such as Easyship at Squarespace checkout. You can decide what rates to display to your customers though - either by setting flat rates or showing variable rates by weight. As you've discovered, the variable rates shown using carrier calculated rates by Squarespace can sometimes vary quite a bit and customers can definitely be turned off by surprisingly high shipping fees in the cart!
I cover how shipping extensions work and how to set up a profitable shipping strategy in this blog post if it's helpful: https://kristineneil.com/blog/how-to-set-up-a-profitable-shipping-strategy-on-squarespace
I didnt try that as I had initially assumed the custom form as part of the checkout function was closer to what I needed.
I will try now and reply back.