You would need to have some customization done to your shipping modules in order to enable and disable them based on the cart content ...

Then, create a new shipping module for the purpose of just the Heavy Category to allow the checkout to complete and state that they will be called with the quote ...

It would also be a good idea to mark these Products in some manner so that the customer knows this in advanced so that there isn't any confusion on the checkout ...

Then on the UPS and USPS shipping modules ... customize them for the Apparel Category to add in a charge for that ...