Yeah, font rendering looks pretty terrible on linux in REAPER at such low font sizes. I've tried a few other font faces on linux as well, but they all render poorly at low sizes. I'm afraid it's something you'll have to live with.
If you want to try and mess with it, I exposed the font face in the following file:
https://raw.githubusercontent.com/Jo...r/Filther.jsfx
None of the ones I've tried looked substantially better though.