I think it's well established that for the basic premise in the Back to the Future Trilogy to work, we have a system of alternate timelines. If this is the case though, then why would Marty in Back to the Future (the original) begin to fade? Logically, there would simply be no Marty in the alternate timeline created when Marty travels back to 1955 for the first time; why should this affect the original Marty from the original timeline?
"I think it's well established that for the basic premise in the Back to the Future Trilogy to work, we have a system of alternate timelines."
If by "alternate timelines" you mean co-existing parallel timelines, so that the "previous" timeline is not erased when the "new" timeline is created, then no, Back to the Future doesn't use that theory. Instead, it uses the model of a single timeline which can be rewritten each time a change is made, and this rewriting can cause the world to transform around time travelers via the ripple effect (like what happened when Jennifer was left on the porch in the altered '1985-A' and Doc reassured Marty by saying "Don't worry Marty, assuming we succeed in our mission this alternative 1985 will be changed back to the real 1985, instantaneously transforming around Jennifer and Einie.") In some cases, this rippling change to the timeline can also erase a time traveler from existence, in cases where they should not have been born in the altered timeline, or should not have lived to their current age. All this is made reasonably clear in the Official Back to the Future FAQ by creators Bob Gale and Robert Zemeckis, when they talk about why old Biff was originally planned to start fading away when he returned to 2015, and also why he returned to the same 2015 that Marty, Doc and Jennifer were in, instead of them remaining in the "original" 2015 while old Biff returns to an alternate 2015-A (the future of the hellish 1985-A created by his giving his younger self the sports almanac in 1955) as you would expect in the co-existing parallel timeline theory:
1.8: What happened to old Biff when he staggered out of the DeLorean in 2015?
The Secrets of the Back to the Future Trilogy A: Our intention regarding old Biff was that upon his return to 2015, he would be erased from existence because he had changed his entire destiny by giving his younger self the Sports Almanac. (Probably, Lorraine shot him sometime around 1996!). After old Biff clutches his chest and staggers (the same symptoms that Marty exhibited in Back to the Future when he was beginning to be "erased"), we actually filmed him falling onto the street and vanishing, and we previewed the movie this way (see The Secrets of the Back to the Future™ Trilogy). However, the vast majority of the audience did not understand it, so we decided to cut it out, leaving the answer ambiguous, and subject to various interpretations — besides the above explanation, you can believe that Old Biff had a heart attack from the shock of time travel of from flying the car, or from something that happened to him in 1955.
1.9: When Doc and Marty are in 1955-A, Doc says they can't return to the future to stop Biff from stealing the DeLorean, because it would be the wrong future. But if that's true, how did Old Biff manage to get back to the same future that he left? Shouldn't he have come back to a different future?
A: As should be clear from the answer to the previous question, we believe Old Biff DID indeed return to a different future — a "2015-A," which would have transformed around Marty, Doc, Jennifer and Einstein (just as Doc explains how 1985-A would change into 1985 and instantly transform around Jennifer and Einstein). This would happen AFTER Old Biff returned with the DeLorean. For this reason, we made sure that Doc had caught Jennifer and exited the McFly Townhouse before Old Biff returned. Thus, by the time Marty and Doc are carrying Jennifer back to the DeLorean, there COULD be other residents in that townhouse — or perhaps the McFlys still live there. It is just as believable that the physicality of the neighborhood did NOT change as it is to believe that it did — so we didn't change it. We decided not to make anything of this idea because this is one of those difficult time travel concepts that general audiences have a real hard time understanding. (Try explaining this stuff to your mother and you'll see what we mean.) A detailed explanation of it would have slowed down the story, and most of the audience doesn't ever think about it. That's why we made certain things ambiguous and left various things open for interpretation in hopes that the possibility of at least one or two explanations would be better than a "definitive" explanation that you could find holes in. Let's face it, time travel is fantasy, so there's no way to "prove" anything. As filmmakers, we try to create a set of rule for our stories and stick by them, and stay consistent within the little "universe" that we've created.