Los Backups hechos con 
Akeeba funcionan perfectamente, pesa 40 MB porque está comprimido.
Si no te convence Akeeba, puedes hacerte un script propio y ejecutarlo con crontab cada "x" tiempo, y que te haga un backup.
Solo se haría el backup de la base de datos, ya que, los ficheros del sitio con hacerles un backup basta.
- <?php  
-  $backupdate = date("Ymd");  
-  //Backup date variable. Replace "Ymd" with  
-  //"Ymd_H-i" to include the time.  
-   
-  $backupdir = "/the/absolute/path/to/the/folder/";  
-  //Where are the files located?  
-   
-  $files = "*";  
-  //What file to backup? Use a * to backup all the files  
-  //inside the folder entered above.  
-   
-  $backupto = "/the/absolute/path/to/the/folder/";  
-  //Where to store the tarball?  
-   
-  $fileprefix = "bak";  
-  //This is the prefix that will be added before the date:  
-  //(bak_20040326.tar.bz2)  
-  //The underscore _ is added automatically  
-   
-  $tararg = "-cf";  
-  //Here goes the tar arguments. I recommend -cf.  
-  //c is for compressing. f is for outputting  
-  //a file.  
-   
-  $bz2arg = "-z9";  
-  //Here goes the bunzip2 arguments. I recommend -z9.  
-  //z is for creating a archive  
-  //and 9 is for max compression. z is always needed  
-   
- //Call the function  
- backupsus();  
-   
- function backupsus() {  
-  global $backupdate,$backupdir,$backupto,  
-  $fileprefix,$tararg,$bz2arg,$files;  
- $backupsuscmd = "cd $backupdir;  
-  tar $tararg {$fileprefix}_{$backupdate}.tar $files;  
-  bunzip2 $bz2arg {$fileprefix}_{$backupdate}.tar;  
-  mv {$fileprefix}_{$backupdate}.tar.bz2 $backupto";  
-  }  
- ?> 
Hay mas scripts como este, solo hay que buscar.