A word from Mr. Paranoid,
To answer your question no, you dont need to back up data that has been previously backed up.
This might seem paranoid but I dont let harddrives sit for extended lengths of time (months and months) without letting them spin up. I work in IT and I have heard techs talk about drives locking up after long periods of time on the shelf. Due to the mechanical nature of harddrives I tend to agree with this. So worst case, you stop collecting and your backup sits on a shelf for a few years. Then you have a crash. You're at the mercy of something mechanical that has been sitting.
I actually have 2 backups and keep one at work ... where I use it. The other sits on a shelf and every month or two I fire it up and do a disk check. Im a PC person and run HD Tune which is a free utility that works well. There are plenty more free utilities and even tools built into the operating system to check drive integrity. The backup at home is pretty much a mirror of my main collection. The backup located at work is always a few months behind. I cant tell you how many failures I have seen over the years ... drive prices have come down but so have the reliability of most of the drives. So my final backup rule is; every 5 years, I swap out the drives one at a time, even if everything is running perfect. So far it's been nice because as HD capacities have grown, I have managed to keep the entire collection on a single drive. I run Western Digital "black" drives but even with their high marks for reliability, I have experienced failures. About a year ago, I lost the drive that held the main collection. My backup was put to the test. Lucky for me; a 5 year warranty and an express return policy had me back up and running in less than a week.
The last rule of a backup system is to test it to see if it actually works
PS - The flooding in Thailand has really caused drive prices to spin out of control. If you can wait 3-6 more months things are supposed to stabilize.