iTunes wants to delete my books I have just lost my laptop, the one that I use to sync all my books. My iBook size is 2.5g an my iCloud account can support 15g.

I tried to backup my iBooks. It shows only 750mb in the backup. When I try to sync my books, iTunes wants to delete them all.

I did not purchase any from iTunes because they don't sell books in my store. What can I do?

My iOS version is 6.1.3, iTunes is at the lastest version.
The most maddening thing about iTunes is it's preference to delete things before. then, syncing them. 

One thing you can do now is to be sure and make a copy of your books folder, perhaps in Documents. You might also back that up to Dropbox. iCloud has not proven itself to be a reliable backup in the cloud, no matter that it syncs quite nicely.

Having said all this, I'm not sure where you are seeing the 2.5GB, and where the 750MB. Generally, one refers to books, or e-books. iBook is a reader, as is the Kindle app, for example. Calibri is, at present, the only real e-book manager for the Mac.