Suppose I use KeePassX as a password manager, and I store the kdb file in Sparkleshare folder as a way for backing up and syncing with multiple devices.
The kdb file in itself would be encrypted, but if someone stole the git repo, they technically would have many versions of the same file with minor variations. Would that in any way reduce the security of the file?
If the encryption algorithm in question is weak against a Ciphertext-only attack, having multiple variants of an encrypted files might allow an attacker to decipher the ciphertext.
All strong encryption algorithms including AES isn't susceptible to such attacks. You should be fine.
Assuming you are using well-implemented, quality algorithms, having a history of the encrypted file should not significantly help an attacker.
However, I would be concerned about insecure versions of the file being kept in version control. For example, if you use a weak password at one point, that weak version could be compromised by guessing the password.
[Would comment on Terry Chia's answer, but don't have the reputation yet.]
