Time machine backup or File Vault encryption of encrypted disk image I have a small encrypted disk image on my Mac (Yosemite), containing account numbers, tax reports and such. I created it using Disk Utility, from folder, which I subsequently safely deleted. I am also doing encrypted TM backups and turned File Vault on - to keep the rest of the files safe.  Could this possibly weaken the encryption of the said disk image on the backup disk or the when the computer is turned off?  (1) Using the login/TM/File Vault password for the disk image (2) Using a different password.

My goal is not to strengthen the encryption of the said disk image; only to make sure it's not weakened. The reason for encrypting it separately is that I want it always encrypted - even when the computer is on and I am logged in.
If you encrypt something once, you can't weaken it by encrypting it another time. You can strengthen it, but not very much that it makes a big difference. Most attacks are brute force password Crack attacks, on both filevault and the disk image, because there is the highest chance for the decrypter to win. So you harden the step of decryption because you encrypt twice, but you don't harden it much. but btw, best anti brute force tactics are using algorithms like PBKDEF2 instead of simple SHA. but that's something only apple can do. and I expect from them to do something like that.