By how much?
There are logfiles, that are immensely useful for troubleshooting, but they're nowhere near big enough to notice on any modern storage device. Even the verbose setting, which is not on by default, isn't *that* big. If you're really that close to full, then you've got some other major issues to work out.
I believe the newest 5 logs are kept and the rest are deleted, if I remember right, so it's not like you'll slowly fill it up......unless you run OBS 24/7 without ever shutting down. THEN you might end up with a 4GiB logfile after a (long) while, just because you're not allowing it to do that housekeeping.