The number one site to visit for weeding is Awful Library Books. This site will show you, with good humor, what you will find if you DON'T weed! The main rule of thumb is that if the book appears on this site, it HAS to go from your library!
There are all sorts of rubrics and guidelines for weeding, but I have not really felt that they quite worked. Like purchasing books, it's a tricky business. But think about why you purchase books-- because they fill a need in your collection, and students read them. Use the same criteria when keeping books.
Here is a good web site, complete with printable book marks and a good acronym, MUSTY:http://www.deeplibrarian.com/free-weeding-printable/
One of my students has been pulling books that meet the MUSTY criteria but which I have kept. The books are old, haven't circulated, are ugly, and sometimes smell, but I have purposefully NOT weeded them. My student asks me one question: "Why are you keeping this?
Smoky the Cowhorse? Stays because it was stamped "August 1969". Not a good reason. Adam of the Road? It won a Newbury, but hasn't been off the shelf in twenty years. The Autobiography of Miss Jane Pittman? Didn't Cicely Tyson make a tv movie of this in the 1970s? This is not a good reason if no one reads the book. If I feel guilty every time I see a book because I can't convince anyone to read it, the book should go.
But James Blish's All the Stars a Stage? Yes, the dust jacket is gone, it only moves off the shelf every five years, it pongs a tiny bit, but it includes this sentence: "You give me a great big fat blue-green fuzzy frozen pain in my starboard rump, Apprentice Admiral O'Kung."
You need to keep some things that amuse you, to add depth, interest, and passion to your collection. Here are some books that I keep because I personally adore them are: We all have things we hold onto, at least for a little while!