AES - Encrypting multiple blocks of files
If you don't allow changes, renames and overwrites then you could create an IV by hashing (e.g. with SHA-256) the unique location of the file. If you want to allow changes/renames/rewrites you could re-encrypt with an IV that also uses the time of the change, if that is unique and stored reliably. That is, if you want to keep the size of the files to the one stated. If you are OK with slightly larger files, it is better to prefix a random IV.

Once you've got your randomized IV then you can encrypt with any secure mode. CBC would be an option, or CTR mode encryption. If you always use exact file sizes then you may be able to forgo padding - only do this if 1KB is the maximum size, otherwise perform PKCS#7 padding. You may reuse your key as long as the IV remains unique. In response to the question, yes, this would be protected against known plaintext attacks.

If your keys are similar then you've got a big problem. You should use random keys or use a password based key derivation function (PBKDF) to derive keys from passwords. Even then, you would require quite a strong password, as offline attacks seem possible.