Well, Alstyle makes a nice medium weight ringspun cotton and it happens to have a tear away label.
The point I was trying to make is you don't have to limit yourself to a tear away if you are sewing your own label in anyway. Most of us use tear aways only because we are printing tagless labels.
I believe gildan, anvil, and american apparel all use the dual label method. Order samples before you take my word on it.
