I was printing a small hardcover book for the game, and when I sent to print it, it tried to charge me $4.5 for the postage of ONE small book.  According to PBS, this small books weighs close to three pounds instead of its actual less than a pound weight.  Does anyone know if all that needs to be done is to submit an edit data to the book team?
 

Yes, just submit a data edit.

The data edit helps the next member who will be mailing the book, but it will take a while to get through the approval process.  For yourself, you can enter the correct weight (either the "book weight" or the "wrapped book weight") on the Print Wrapper page.
 

It is best not to print a wrapper with postage if the weight is off. Enter the correct weight either for the "book weight" orfor  the "wrapped book weight" on the Print Wrapper page, then print the wrapper. The cost for printable postage using PBS money once the wrapper has been printed in non-refundable. You can read more about this in the Help Center by entering "printable postage" in the Search Terms window in the Browse Help  Docs section.

Most of the time PBS will have the correct or near-correct weight listed, but sometimes it is off by a lot and sometimes off by only a little. Personally, I use printable postage and always check the book weight using a postal scale I have on my desk and then adjust the weight if needed before printing the wrapper. A kitchen food scale should also do the trick. When dealing with ounces, always round the weight up to the next whole integer so that 5.2 oz or 5.7 oz, for example, should be rounded up to 6 oz.

Postage varies by the ounce for book weights under 7 oz. and will be mailed First Class.  Similarly, book weights between 7 oz. and 16 oz. will be rounded up to 1 pound and will be mailed with Media Mail postage, and book weights between 1 pound and 2 pounds will be rounded up to 2 pounds and also mailed as Media Mail, etc.

So, in cases where the weight is anywhere between 7 oz and 16 oz, or between 1 pound and 2 pounds, the precise weight is not critical since for the postage purposes the number will be rounded up to the next whole integer pound.  Package weights over 1 pound, even as little as only 1 oz over, need to be rounded up to 2 pounds. So, it is only for book weights less than 7 oz, or very near 1, 2, or 3 pounds, that the exact weight may come into play.