I doubt there's a "we" that can answer your question -- it all depends on your specific requirements. If, for some reason, you want to be able to restore the image of your data as of exactly 7 days ago, but not 6 or 8, sure, hold on to your weekly backup.
If, on the other hand, powers that be require you to be able to provide a snapshot of your data at any instant within the last seven years (this happens), you have a choice.
You can keep just one base backup taken at the beginning of time, plus all of the transaction logs since then, to facilitate point-in-time recovery (PITR). Recovery, though, might take about the same time that it took to run all the transactions, consecutively, since that first backup, as you'll be replaying all the logs between then and the recovery target time.
Alternatively, you can keep daily (weekly, monthly) backup images, plus all the logs for the next day (week, month), in which case you'll use more space but your recovery time will be reduced proportionally.
If, however, you don't have these "go back in time" requirements, you don't really need to keep more than one backup image, taken with the frequency that your RTO (recovery time objective) demands.