Time Machine Backup Failed, don't have old backups

Question

Last night I ejected my external hard drive to use that USB port to plug in a card reader and download a bunch of videos and images. This afternoon, when I plugged my external drive back in, I got a Time Machine Error: "This backup is too large for the backup volume". When it tries to back up, I get the more detailed message that this backup needs 6.7 GB of space but there are only 6.2 GB available.
This is the only computer I've ever attached to this external hard drive, so the 49.38 GB that are currently being used should be being used by Time Machine to back up this computer (and so Time Machine should delete old weekly backups to make room for the most recent backup). However, when I open Time Machine to go look at my backups, it says I only have one backup, from last night.
I do like the fact that I can go restore old stuff I've deleted or disastrously edited, so, if possible, I'd like to get my old backups back. Failing that, I guess I need to clear the external drive and just do a new back up.
If someone can help me 1) get my old back ups back or 2) get Time Machine do a successful completely new backup, I'd be really grateful.

Answer 1

My first reaction was that that couldn't possibly be the problem (because I've had no problems at all backing things up for the past year and a half), but it appears that you are correct.
Apparently, all of the pictures and videos are, in fact, too much for my Time Machine external hard drive. I don't have anything else on the external hard drive, but my TM drive is, in fact, much, much smaller than my internal HD.
Time Machine Backups
Capacity: 55.57 GB
Available: 6.19 GB
Used: 49.38 GB
Macintosh HD
Capacity: 232.57 GB
Available: 175.45 GB
Used: 57.12 GB
I see the problem. I guess I'll move all of the videos to a folder that I can exclude from backups. (I much prefer to have excel spreadsheets I put data on every day backed up than blizzard videos shot with my spouse's camera: those I can lose.)
I was so certain that I wasn't running out of space that I didn't check, so I was thinking that I should still have old backups. Since they've been deleted, that's fine with me.
Thanks for asking me to check the relevant sizes!