Can CBC-encrypted files be modified in-place? When changing a (small) part of the plaintext of a CBC-encrypted file, how much of the file will have to be rewritten?

My suspicion is that everything after the modified block will have to be decrypted and reencrypted as well, due to the changes of the ciphertext blocks cascading through the rest of the file.
If you could use the same IV, then yes, you would need to rewrite everything after the modified block.

But you shouldn't do that; every time the contents change, you should generate a new IV, which would require the whole file to be rewritten. Otherwise an attacker can learn more information than it should about how the file changed (precisely by checking which blocks of the file have changed).