What is logging to /var/log/sa6 on BIG-IP DNS and filling up /var/log partition?

These files are produced by the linux sar utility (system activity report) process. They're not big-ip specific, and contain historical data about system activity - cpu utilisation, memory usage, disk activity, etc.

I'm not sure why you're seeing such large files, as that's not typical.

You can delete them, as nothing uses them (yet). I recommend you open a support case to investigate this more thoroughly, as we'll need a qkview to start figuring it out.