As “Gtk-WARNING Default font does not have a positive size” suggests, this arises from a font size specified incorrectly, or not at all in some cases. This problem annoyed me for a while after using a few different window managers with Linux (Ubuntu in particular). I believe it came about after changing some font settings and changing themes a few times, particularly with LXappearance. I’m guessing if you are looking at this you have also made a few changes and are now also being annoyed by this message!
The Problem
You will see this annoying message, repeated numerous times in the terminal, when launching applications from a terminal:
Gtk-WARNING **: Default font does not have a positive size