Before you flag my question as already answered, please note that I am try to see the text in "Ubuntu Browser," not Chrome or Firefox, etc. Ubuntu Browser has a desktop icon that is a blue map of the world with a compass needle overlay. I intalled it from Ubuntu Software. The text in Ubuntu Browser is too small for me to see using a 24 inch monitor. I can adjust the font in Chromium and Firefox and on the Ubuntu desktop and system. I can not find a way to adjust the font in the web browser named "Ubuntu Browser." Ubuntu Browser may be a newer app for Ubuntu 16.04. Thanks for you help!
I don't think the Ubuntu browser zooms at this point.
There are tweaks and hacks for zooming/magnifying the screen (Zoom desktop tool for Ubuntu 14) but I doubt these will satisfy you.