I worked at The UPS Store for two years. If a customer dropped off a box with a pre-paid shipping label that had the wrong weight on it, it would still be delivered and the customer would be billed the difference directly to their account. And even if you paid The UPS Store to ship it instead of putting it on your own account, and it had the wrong weight on it, they still would go ahead and deliver it, then bill that UPS Store the difference. UPS does not bother to return the package simply for having the wrong weight billed on it under basically any circumstances.