Q: Last iCloud backup=22 weeks ago.

Hello, not.a.techie. 

The most common cause for the unable to backup alert due to exceeding the free 5GB storage allotment is photos and videos taken with the device.  I would recommend importing there to your computer and deleting them from the device.  You do have the option to sync them back to your iPhone through iTunes once imported.  Here are the steps on how to import and after completing a backup syncing via iTunes. 

iOS: Importing personal photos and videos from iOS devices to your computer

http://support.apple.com/kb/HT4083

You have the option to purchase more storage if needed.  However, if that is not a desired option, here are some helpful steps to troubleshoot this issue. 

I can't back up because there's not enough storage available.

If your iCloud storage reaches its maximum capacity, you can take any of the following actions:

• Purchase more storage.
• Create a smaller backup. Tips for creating a smaller backup:
  • Select which apps to back up. Include only the apps that contain important data.
  • Reduce the size of your Camera Roll backup by deleting unwanted photos and videos before backing up. Optionally save the photos and videos to your computer before deleting them.
  • Turn off backup for Camera Roll, especially if you already back up your Camera Roll to your computer.(Your iCloud Photo Stream is not a backup of your Camera Roll.)
  • Delete old messages from your device, especially messages with attachments. To delete a message, swipe over it, then tap Delete.
• Delete items that you no longer need from iCloud, optionally saving them to your computer before deleting them. For example, you can:
  • Delete old backups, such as backups for devices you no longer have.
  • Delete app data or documents.
  • Delete old email messages, especially messages with attachments.

iCloud: Troubleshooting creating an iCloud backup

http://support.apple.com/kb/TS3992

Cheers,

Jason H.