I determined the issue lies probably in syslog and user.log as they are the biggest files in that folder with 1.6 GB each. On top of that, I could significantly slow the disk space usage growth down by disabling the rsyslog process.
Looking at the last lines of syslog with tail, shows me this example line (the hex number and the id are sometimes different in that file)
and looking into user.log shows me this example linegnome-shell[1011]: /build/glib2.0-B1uXKV/glib2.0-2.50.3/./gobject/gsignal.c instance '0x557fbe981220' has no handler with id '47253'
I am using Debian Stretch 9.2 with gnome./build/glib2.0-B1uXKV/glib2.0-2.50.3/./gobject/gsignal.c instance '0x557fbe981220' has no handler with id '47253'