Hi, GT,
My understanding of lines is this: A double taper 6 weight and a weight forward 6 weight both weigh exactly the same "should" both will work with your outfit to some extent. Keep in mind, however that while both weigh the same, their taper is different. It is somewhat common that a weight forward line ONE WEIGHT HEAVIER than specified, will work better with a rod. So, a WF7 may be in order for your 6 weight rod. This has to do with weight distribution in the line and how it functions to load the rod.
Weight forward was designed to cast longer distances, while double taper will cast more accurately, but at shorter distances. Gene is correct that double tapered lines can be reversed and you, virtually have a "new" line. So I consider them more economical.
With all this said, everyone's casting style is different. How one casts the fly rods they own is often a determining factor how well a specific weight line performs on a given rod.
If one of your friends owns a 6 weight outfit I'd ask if you can cast their weight forward line on your rod. If it seems to cast okay, you're in business and can get a similar line. If you have trouble casting out the weight forward line-like the line is very soft or "jello-y" then you may need one size heavier in the weight forward taper.I f you know someone with a 7 weight weight forward line, give a test.
A DT6 should, generally handle quite well with your rod without testing.
I have used Cortland 333 fly line for many years and would highly recommend it to anyone. Cortland currently has them on sale through their outlet store. Check the link below.
Cortland Lines
Mark