If your motivation is tone you are not going to hear any difference from a more massive nut to a less massive nut all other things being equal. By equal I mean more specifically making say a bone nut and not perhaps using brass.... which is so last century anyway....
Instead a well fitting nut firmly sitting on wood with well cut slots that don't bind, have the face of the slot be the break point so that you don't have the vibrating wave breaching the nut slot face(s), and individual slots cut well also meaning not too high which can impact intonation.
3/16th" is fine and a nice size IMO to make look eloquent, highly polished, and with minimal additional mass so as to not look chunky...
When I started building and repairing my nuts were much more chunky than they are today and no jokes please.... well maybe a few. The old adage form follows function IMO applies to nut making as well.
Just read Ken's excellent post too: There are some of those space aliens, or should we say undocumented extraterrestrials that can hear such things.... From the differences in the electrons that a pup battery of one brand over another produce... to that $20 vintage cap that will turn a fair player into Clapton I sure wish that I could hear these things too...
Disclosure: I am one of the ones who turned up my nose at stainless frets thinking that they sounded "tinny..." Last summer I took a blind test with an ax with NS and stainless on it and could not successfully guess a single stainless fret....
Since this was an electric now I am saying that I can hear the difference on an acoustic only and sticking to my story.... 
