If you are creating FULL backups, then each TBI file contains the complete backup data from the date you created it. You can delete the older TBI files if you have a more recent one that was also created from a FULL backup (but you should make sure the more recent ones are valid before deleting older ones - using TBIView to browse a TBI file can help).
However, if you are creating CHANGES ONLY backups, then you must keep previous TBI files until you create the next FULL backup, since the CHANGES ONLY backups are dependent on previous TBI files (either on the TBI file created from the last FULL backup for "Differential" changes, or on the chain of previous TBI files created from "Incremental" changes - see this thread viewtopic.php?f=4&t=2978
for (hopefully) a clarification of the difference between the two types of CHANGES ONLY backups.
A separate issue: Your post said "my backup device" (meaning singular - ONE device). If at all possible, you should have more than one backup device. Ideally, you should create multiple copies of each backup. But at minimum, you should alternate your backups to different devices, so that if one backup device goes bad, you have another (though probably older) one to restore from - "Don't keep all of your eggs (backups) in one basket (drive)."
Also, it's best to keep at least one device in a different physical location from the others (if this is a home computer, then take one backup copy to work, or a relative's house, or a storage locker (assuming it's climate controlled), etc.). The idea being that if something happened at your home (fire, theft, etc.), you would have a backup elsewhere that you could recover your data from. If you're concerned about storing your personal data in a location you don't control all the time, then consider using the encryption option in Image to keep someone from accessing your data when it's not stored at your home (of course, you may want to encrypt the copies stored in your home as well, it all depends on the type of data stored).