Sher,
What the post office does is charge the customer the flat priority rate of $4.05, they deduct the postage you already paid for first class mail and charge the customer the balance.
I had a customer to whom I sent art in a CD mailer and used peanuts to bulk it up. She has had an ongoing feud with her local post office for some time (after she objected to some very shabby mail handling practices). The package arrived at her home squashed flat and a postage due of several dollars. It seems to me the local postal people deliberately squashed those peanuts so they could stick it to her one more time.
The solution to that is the customer should refuse the package, it will be delivered back to you free of charge (one of the benefits of first class mail), and then you can resend it... you're still out the extra postage to remail it, but it's much less than paying the highway robbers the priority rate. Of course the dilemma is most customers wouldn't know to refuse it, they would just pay it and tell you after the fact... but since this had happened to this person before she got wise to their ways.
And just remember with the new rates coming up, the thickness is going to need to be 1 inch, not 3/4 inch as it is now. And hope that somewhere along the line someone doesn't squash yer peanuts flat.
Denise