Which compound algorithms would weaken cipher, not strengthen it?
Moving my reply from the comments into a proper answer. The general case of double-encrypting is formally explained by Yehuda Lindell in this answer on crypto.SE. Summing up:


Same Algorithm, same key: It may or may not be secure, depending on the properties of the cipher. It is definitely not always secure, but may be secure for practical cases.
Same Algorithm, different keys: Secure, because otherwise people who do not know the key could break the encryption by encrypting with a different key, which would be... strange, and not very logical.
Different Algorithms, different keys: Secure, for the same reason. Otherwise, sending PGP-encrypted eMails over a TLS connection would be unsafe, which would be ridiculous.
Different Algorithms, same keys: Insecure. Never reuse keys for different encryption algorithms (even when not double-encrypting). For example: If you are using the same RSA keys to sign and encrypt, and the adversary can get you to sign a value for them, it can use you to decrypt data, because signature = encryption with the private key = decryption of data encrypted with the public key.


Summing things up: "Don't double encrypt" is a pretty general hint that definitely doesn't always apply, but it serves as a good baseline to avoid critical mistakes. The more nuanced version is "Don't reuse keys for different algorithms, and to be sure, don't double-encrypt with the same key and algorithm, either, it may hurt you".