Now, I know that armor bonuses don't stack, so lets get that right out of the way. However, if I were to wear Quilted Armor (from the APG) under heavier armor would I still get the benefit of the DR3 vs small ranged weapons?
In my home game I would be inclined to allow it but with a massive dex penalty.
The only case this could come would be wearing it under an Armored Coat, given that that is the only armor that can be worn on top of another. In that case, the coat says to use "the better AC value and worse value in all other categories." So it will depend on whether you consider "DR vs. small ranged weapons" to be a "category," or if "category" is only those things listed on the armor table.
I'd probably go with the second interpretation, myself. It isn't a game breaking combination or anything, and it wouldn't make sense for the Quilted Armor to become worse just because you had a coat on over it.
I would allow it, but I would impose a -4 on any save or other rolls that dealt with heat effects.
Since every armor but full plate was worn over a quilted gambeson, I don;t see why there'd be a problem, except that maybe the gambeson is also considered.
This is an actual historical armor, one of the reasons Mongols kicked so much ass is the they went everywhere with quilted silk longjohns under their armor. Enemy arrows where stopped or vastly slowed by enemy archers.