The SDMB fonts are contained within a stylesheet. Adjusting the font size in the stylesheet for one type of display is possible, but cumbersome and time-consuming since it’s a generic stylesheet. You should look at your device’s configuration settings to see if you can make changes on your end.
I had the same issue with my Nexus 7. It seems to go away when I hold the device on its side to display in landscape. I am pretty sure it has to do with the font scaling that Chrome uses on Android devices. I’ve had the same issue with both 4.3 and 4.4. I ended up downloading the dolphin browser and using it instead of Chrome at one point.
Oddly enough, I recently uninstalled and reinstalled Chrome and the issue seems to have gone away.