We don't have tax deductions for this sort of thing over here (more's the pity), so I tend to give unwanted books to Oxfam or one of the other charity shops that abound. And, as I've said before, we have Public Lending Right, so British authors do get a crust or two on the basis of public-library borrowings.
But, leaving aside libraries, are books different from other commodities that are sold second-hand? Suppose I buy a CD player, decide after a while that I'd like a bigger and better one and sell the old one to a second-hand shop. No-one complains that the inventor or designer isn't getting a cut.