I am certainly not an expert, but from what I've learned, it would seem not at all. 7700 dry i would guess is at least 9k loaded. Is that dry weight the "listed" weight or sticker? There should be a yellow sticker giving you a more accurate weight. This often does not include propane, batteries, water etc. What is the max payload of the suburban? you'll likely be over that as well with that much TT.
also, are you just moving it 1-time up to WA or are you hoping to do more travelling with it? a one-time move, might want to hire someone to get it up there. More travel i think you probably need more truck. But i have a much smaller TV and TT, there are plenty others on this forum who can give you better info.