Finley from Shopify here. Thanks for your question!
Are you using Shopify shipping to print your labels from your Shopify admin?
If not, and you're instead using a third-party app for shipping, you'll want to reach out to their support team to confirm how their app calculates the shipping costs your customers pay vs the shipping labels you're paying for.
Printing shipping labels with Shopify shipping
After an order is placed, you'll be able to print a Shopify shipping label, as long as your business is located in the United States, Canada, or Australia.
When you print a label, you can select which box you'll use to ship the order.
If you're offering calculated rates
If you're offering Shopify shipping's calculated rates at the checkout, the amount that your customers pay for shipping will be determined by the weight of your product(s), the dimensional weight of your default package, and the shipping carrier selected.
You can double-check your product details to ensure the weight of each product has been entered correctly.
You'll also want to ensure that your default package's dimensional weight is one that would work best for most of the orders placed on your website.
The dimensional weight can be adjusted under your Shopify Admin > Settings > Shipping and delivery > Packages > Saved packages > Edit like so:
With calculated rates, you're also able to discount your shipping rate by a flat fee or by a percentage of the total shipping rate by editing the handling fee. Alternatively, if the rates were too low to cover your packaging costs, you could at an additional fee.
If you have flat rates or free shipping
If you're using a flat rate or offer free shipping, you can adjust these rates to something that would work better for your business and customers.
You can adjust this under your Shopify Admin > Settings > Shipping and delivery> Manage rates > Rate name > Edit rate
If it's important for you to be able to assign different box sizes to different products, instead of having customers pay based on the default box size, you can have a look at some third-party apps on the app store such as:
If anything is unclear or there is something I haven't touched on, please let me know and I'll be happy to clarify.