It may have been bought precisely to be given away, or it may have been an old favorite handed over, dog-ears, fingerprints and all. You've offered something that means something to you, asked them to share it with you, waited to hear whether it means something to them as well. It's generosity and ego, an opening of doors and a plea for validation. It's constructing a bond. And then the bond breaks, and the book is still sitting there.
Books have weight, when they come from people who matter.
There was a collection of poems once, given to a young man about to set off for college. But that's so efficient, so cold. There's got to be another way. You've liked it enough to want to keep it for yourself, you make clear, and enough to think he or she might want it, too. That's so pleasant, so reasonable.