Problem about backup software

I have Acronis True Image 2013.
I backed up my whole C:\ disk two months ago, and now I need to update the backup. So I opened Acronis and set an incremental backup, but the program stopped because there's no more space in the backup disk.
Disk C:\ is 500 GB (really 430, there is also a linux partition) and the destination disk is an external hard drive of 500 GB too (also 430 and not 460, Idk why).
Theorically the incremental backup should upgrade not using more than the used space, but in my case the operation stopped, as I said. I do not know why it happened, two months ago I set the program in order to do future incremental backups.
Can anyone help me to find where I did a mistake?
If not I would be glad if you can tell me if there is a program that does what I need: simply backups, not necessary of the whole system -I would use it also for my others internal disks- that are upgradable but they don't need more space than the using disk. For example, years ago I used Freefile Synch with the mirror option, that was good too, but once it suddenly gave me the same problem.

tl;dr
Need a program for backups, that simply upgrade the old backup file withouth using more space than disposable, and deletes the old files. 500 GB -> 500 GB

Thanks in advance

I use Macrium reflect myself. The only area I can think of that you may have 'gone wrong' as you say would be that some backup programs have the ability to backup unused space. That would be the difference between 'Image' and 'Backup' an image is usually synonymous with cloning which will make an exact duplicate, unused space an all. So if you have a partition with say Windows on it that is 80GB but the System and user files are only using 30GB, cloning will create the whole 80GB on another disk same as the original.

I use Redo Backup to make an exact same duplicate of my OS after doing a clean install, updating and installing some fundamental software like AV/SpywareRemoval/Firewall. But as Richman said, that clones everything, although I differ on the size of the resulting image in comparison with the size of your partition. If you use Redo Backup, to make an image of your system before installing more stuff, say your partition is 500 TB, and you make a backup, the resulting image will not weight 500TB, the program selects your files and the system files, and it tells you what will backup and what not and the program doesn't take in mind unused space. The UI is really simple and frendly, you should try it, it's based on Clonezilla, both are excellent programs. But I'm unsure if the program itself will let you update an existing image. In any case, try them both, they are open-source and free to use.
Redo-Backup:
Redo Backup Bare Metal Restore Solution GUI Backup Open Source GPL Recovery
Clonezilla:
Clonezilla - About

Thanks you all for the excellent answers you gave me.
I didn't know Redo Backup, which seems to to be a very good software for emergencies. I'll try it, even tough it appears that it has not the incremental backup (at least clonezilla hasn't, so I think Redo too.).
Looking at my needs and your answers I think that it would be better to use a synchronizer software.

The best experience I had until now was with the aforementioned FreeFile Synch. Using the Mirror option the program synchronizes my files between the source disk and the backup disk deleting the files I deleted on the source.
The problems I had with FFS were two:
1)The software compares the two disks every single time, and this task takes a lot of time. In this video we see the creation of a batch files. Does it accelerate the task?
2)Even if it does a comparison before doing the real backup, it still asks for more space than I have - I presume it's due to temporary files(?).
I have also seen Synctoy in a similar topic, is it better than FFS?
Thanks

Before deciding on which software to use you really need to decide whether it's simply a file backup you want or whether you want to be able to restore your system should it become unbootable or seriously infected. As you had initially used Acronis to image your C drive I assumed it was the latter but not sure at all now. If you can answer that question there is loads of choice available for either or both routes.

wakk said:

The problems I had with FFS were two:
1)The software compares the two disks every single time, and this task takes a lot of time. In this video we see the creation of a batch files. Does it accelerate the task?
2)Even if it does a comparison before doing the real backup, it still asks for more space than I have - I presume it's due to temporary files(?).
I have also seen Synctoy in a similar topic, is it better than FFS?
Thanks

1: How do you define a "lot of time"? I use FFS to backup 127,000 (590 GB) files at least once a day. The comparison process takes just about 60 seconds and the actual writing of new files and deletion of old files rarely takes more than 3 or 4 seconds. The entire process has never taken more than 70 seconds, with a single mouse click.

I use the batch file method, but I don't recall it's any quicker than any other method. I don't see any reason why it would be. It's just convenient.

2: it does use temporary files as do the similar programs I have used. If you are in a jam for space on your backup drive, you just need to get a larger drive or whatever is necessary.

Synctoy, FFS, and all similar programs work in about the same way. They differ primarily in their interfaces and in how easy they are to learn and operate. I wouldn't expect significantly different results if changing from one to the other.