Krachen makes pertinent comments about his opinions on the use of 7x and lighter/finer tippets. I agree with him 100%. One should not be attempting to use 7x unless they have gained significant river and fish fighting experience with 6x. I do not like to leave flies in fish when 7x breaks. I don't know if it really does any harm to the fish as I often catch fish with one or more flies in their mouths. I however love these trout and don't want to leave them in a state other in which they were prior to my fishing for them.
I don't condone using 7x often and I have never used it on the main stem of the Delaware. While it may be harder to fool those big rainbows rising to Tricos on summer mornings or sucking in little Sulfurs and olives on those flat pools during a summer afternoon it is foolhardly to think you have as good a chance to land one on 7x as compared to 6x.
There was a one week period in late July where even my most perfect casts with 6x did little to enticing the WB No Kill browns to rise to any of my offerings. When I switched to Rio 7x I immediately began hooking up fish. I lost more fish to the hook pulling out than to broken tippets. I set the drag on my little Teton reel to almost the lightest setting - the spool revolves freely. I use either a 8' 6" or 9' rod for a DTF #4. When a fish eats the fly I let the fish close it's mouth and complete the rise before I just lightly lift the rod to initiate the contest.
Lastly there are sections of the river where one can actually study not only the rise form but one can also see the size of the quarry. I would be more likely to make a cast to a 12" - 15" brown with 7x than I would to a fish the 16" and larger class.
As soon as the difficult period ended I immediately went back to 6x and had a couple of days where I caught so many large fish that I can't even post the lengths for fear you will consider me to be testing the limits of your credulity.
Presentation, getting as close to the fish as possible, timing, and proper fly selection is far more important then going to 7x. Many of my 20" and larger Delaware River fish are caught on 5x. The photo demonstrates one of many large browns taken on the Delaware system on tippets heavier than 7x.