From the PBS Help Center:

• Our database is compiled elsewhere, and it includes some inaccuracies, including the weight of some books.
• The weight of a book as recorded in the PBS database determines the "recommended postage" that appears on the PBS wrapper.
• If the book itself weighs close to the "pound" mark (very close to 1 lb or very close to 2 lbs, for example), the Wrapping materials can actually put the wrapped book into the next higher postal rate. 
• You can see the estimated weight on the Wrapper Settings page that comes up when you click Print Wrapper on the request.
  • You can adjust the weight there and the postage that will print out on the wrapper will change accordingly.
  • This will not change the weight of the book in the database; it will change the weight of your shipment.

PBS, does not bump the rate for packaging, you are supposed to include that in the number entered (it says package weight). All of the rates are for Weight Not Over X lbs so $2.13 is UP TO 1lb, $2.47 will kick in at 1.01lb.

I just printed out a label for a book, and it kept calculating for First Class, even though I changed the weight due to a second book being added to the package.  This one goes to the PO.

Bonnie anything up to 7oz will get a FC wrapper.

I noticed the First class thing the other day on a book.  It changed it to first class even though it was 2 cents more.

Chris, will it stay first class, even though I changed the weight to 1 lb 6 oz? 

Are you sure you put the 1 in the lb feild. I ask cause I have left it out before (a couple times)

The two cent difference is done cause for two cents more your sending the book sometimes twice as fast.

I'd pay the two cents more to send First-Class - will get there quicker  as First -Class is not supposed to get put aside during heavy mailing periods,  and avoids any possible delays that might happen when sending media mail due to inspections. 

It'll usually choose first class if it's 2:15 over the 2:13 media mail. 

I was having the same issue I KNEW the weight listed for the book was wrong and wanted the Media Mail label not First Class but the system kept resetting it for First Class didn't matter what I tried.  I ended up sending the book first class for another $.19.  I emailed the PBS Team and they responded looking for specifics I don't know if they ever figured out what the problem was.