Time Machine error: not enough space

Question

A little while ago I got an error from my Time Machine backup, stating, "The backup disk needs 349.72 GB for the backup but only 327.67 GB are available. Select a larger backup disk or make the backup smaller by excluding files." This was not a new backup, and I couldn't see any reason why Time Machine would deviate from the usual small incremental backups. I finally ended up formatting my Time Capsule and starting over. Things were going fine until today, when I got the same message. Any idea why this is happening and what I can do to fix it?
The backup is for my iMac, running OS 10.10.3, the Time Capsule is 1 GB. I don't have any partitions, and the total backup for my computer should be only around 500 GB according to the Time Machine preferences. I do have an external hard drive connected, which holds videos and photos and is included in the backup.

Answer 1

Thanks for the comment but I don't think I'm having any of those issues. Time Machine will work fine for a while, and then it suddenly decides it needs to back up almost 350 GB of "new" data even though there haven't been any changes that would justify that large a backup. This is what I see in the Time Machine Buddy widget:
Starting manual backup
Attempting to mount network destination URL: afp://Jeremy%20Weiss;AUTH=SRP@Jeremy's%20AirPort%20Time%20Capsule._afpovertcp._ tcp.local./Jeremy%20Weiss's%20Time%20Capsule
Mounted network destination at mount point: /Volumes/Jeremy Weiss's Time Capsule using URL: afp://Jeremy%20Weiss;AUTH=SRP@Jeremy's%20AirPort%20Time%20Capsule._afpovertcp._ tcp.local./Jeremy%20Weiss's%20Time%20Capsule
Disk image /Volumes/Jeremy Weiss's Time Capsule/Weiss's iMac.sparsebundle mounted at: /Volumes/Time Machine Backups
Backing up to /dev/disk3s2: /Volumes/Time Machine Backups/Backups.backupdb
Will copy (602.4 MB) from Macintosh HD
Will copy (Zero KB) from My Book for Mac
Found 157930 files (327.16 GB) needing backup
350.45 GB required (including padding), 327.67 GB available
Ejected Time Machine disk image: /Volumes/Jeremy Weiss's Time Capsule/Weiss's iMac.sparsebundle
Compacting backup disk image to recover free space
Completed backup disk image compaction
Starting manual backup
Network destination already mounted at: /Volumes/Jeremy Weiss's Time Capsule
Disk image /Volumes/Jeremy Weiss's Time Capsule/Weiss's iMac.sparsebundle mounted at: /Volumes/Time Machine Backups
Backing up to /dev/disk4s2: /Volumes/Time Machine Backups/Backups.backupdb
Will copy (602.6 MB) from Macintosh HD
Will copy (Zero KB) from My Book for Mac
Found 158025 files (327.16 GB) needing backup
350.45 GB required (including padding), 327.67 GB available
Deleted backup /Volumes/Time Machine Backups/Backups.backupdb/Weiss's iMac/2015-05-02-084159.inProgress/2A826121-7477-4D3F-A86A-FE5FFEEC0B19 containing 4 KB; 327.67 GB now available, 350.45 GB required
Deleted backup /Volumes/Time Machine Backups/Backups.backupdb/Weiss's iMac/2015-05-02-084159.inProgress/5BF1ECEE-6819-4A94-A9A3-7DB133F7D617 containing 4 KB; 327.67 GB now available, 350.45 GB required
Removed 2 expired backups so far, more space is needed - deleting oldest backups to make room
Deleted 2 backups containing 8 KB total; 327.67 GB now available, 350.45 GB required
Backup date range was shortened: oldest backup is now May 2, 2015
Backup failed with error 7: Not enough available disk space on the target volume.
Ejected Time Machine disk image: /Volumes/Jeremy Weiss's Time Capsule/Weiss's iMac.sparsebundle
Ejected Time Machine network volume.