Even thou additional rules for armor types aren't explicitly written, you'll always fallback to the Fictional Positioning: maybe you can say it is Impossible to be stealth with a heavy armor, or flee from an unarmored foe.
The Disadvantage case is also covered, as you just need to consider the PC as poorly equipped.
In these examples, I think it is all the GM's preference, so no futher rules are needed imo.
One last example you'd want extra pieces of armor is with the Scrap Fighter ability :P