When you say "weapons" that's a big subject. If you mean only small arms that's one thing but "weapon" would also include artillery; not sure if you are making a distinction.
For a nice introduction that you can get in paperback for cheap I'd say start with:
Coggins, Jack. (1990). Arms and Equipment of the Civil War. (Dover Publications, Mineola, New York).
It has line drawings and is only a 150 pages or so but is remarkably detailed and is often referenced in bibliographies; a classic. If you want to delve into only small arms or artillery (which actually has several sub-genres: field, siege, naval) then there's classic works that address those specifically in detail.