According to this page ( http://www.st-v-sw.net/STSWvolumetrics.html#mozTocId859859 ) at a SW vs ST website (which agrees with Nob that Enterprise displaces a million tons), the 190,000 ton figure appeared in TOS writers guide, from where it was included in The Making of Star Trek and FJ's Technical Manual.
Anyway, I'm comfortable with having starships constructed like naval vessels and having similar densities. I've used that assumption in all my work. After all, lighter and less-dense ships should be easier to build and operate, and advanced materials should be lighter yet stronger than what we have now. But if any of you want to believe that Enterprise was 5 times as heavy, that's OK too.
