if you want some specific advice on flyflishing, western or tenkara, I'm happy to help. PM me some time. I'm a flyfisherman first, and backpack to indulge my habit, rather than fishing occasionally when I backpack.
Some insights are:
the gear need a slightly different focus for a person going bakcpacking to flyfish, than someone going backpacking with the option of flyfishing. for example, you need warmer clothes for fishing than walking, you don't use your base camp warms when fishing (sooner or later youll go head over heels), and thus you need to re-think the gear approach (e.g. go polar fleece etc for day wear, and skip the base camp downs, but increase the rating of bag - you stay in gear that can be soaked and then strip down into a higher rating bag). And, if your goal is to flyfish, then some choices are different compared to having the option of fishing when backpacking.
And, you'll need to think about wading, especially if fishing shoulder seasons, on some rivers. And what this means in terms of gear and exposure to elements.