Re: If you encrypt something more than once...
I wouldn't think that re-encrypting (with different keys) would weaken the crypto in any way. If it did then the first thing a cryptanalyst would do with ciphertext would be to encrypt it again to introduce that weakness.
The main benefit of repeating the encryption is that if for example you do it twice, then you have two keys, and therefore double the total key length.
DES is algorithmically secure. There are no known attacks faster than brute force. Unfortunatly DESs 56 bit key size (64 - 8 checksum bits), makes it computationally feesible to brute force the key. 3des makes the key 3 times longer, so its currently safe, but slow.
I dont see any benefit in encrypting twice using AES-128 both times over using AES-256 once. In this example(situation described in article), I dont see the benefit in what is effectively them having half the key, and you having the other half. Having that said, from a defence in depth perspective, Its a good strategy to defend against both known, and unknown/imaginary threats. Googling for "This was fixed six months ago in OpenBSD" should illustrate my point.