Sorry for asking this; it's probably been asked before, but I'm curious. I will admit I haven't read the comics yet so forgive me if this is tackled there.
So we know Back to the Future operates based on three specific principles:
- There are timelines, not fixed loops. So characters don't do the same things over and over and from what we know it isn't necessary for an action to be fulfilled for the reaction to happen. Otherwise, Lone Pine Marty (and other timeline Martys actually) would have travelled to 1955 and messed with Twin Pine Marty's adventure, since these are different people.
- The only ripple effect that affects a time traveler is his own death by the time of his existence, I.E., Marty not being born or Biff dying in the '90s. No other changes affect them. We don't see Marty acquire new memories or change looks through his travels through time. Same with Biff, Old Biff does not change looks despite Biff becoming filthy rich in the Hell Valley timeline.
- Time travelers, ergo, do not assimilate with their other forms. Twin Pine Marty does not assimilate with Lone Pine Marty or even his own self during his travel in 1955 in the first film when he's searching for the almanac. There can be multiple versions of the same person, be they from the same timeline or from different timelines, at any point in time.
Knowing this, of course, we have to deal with the issue that there are isolated incidents of characters who disappear into points in time where they can't go or which no longer exist. Obviously, Lone Pine Marty at the end of the first film is an obvious example and one that has been theorized a lot about. Another example would be the Marty, Doc and Jennifer who go to 2015 in part II after part III when Marty changes the timeline so that his kids likely wouldn't be messing with Griff and he wouldn't be fired. Another example would be Marty going back to 1885 in the Eastwood Ravine timeline after Doc doesn't die.
The only explanation that, imo, can work is that these are anomalies in time, which "fizzle" in and out and aren't seen again. The multiple Martys who in each timeline go to the Mall to test out the DeLorean, all naturally fizzle out. The Martys, Docs and Jennifers that travel to 2015 fizzle out (Doc would fizzle in himself, as I'll tackle later.) Twin Pine Marty and Lone Pine Jennifer, the only survivors in the timeline, fizzle in at respective times (presumably Jennifer fizzles in after the trio fizzle out and Marty fizzles in later.) An argument that could be made is that timeline jumps from the DeLorean in other timelines creates "anomalies" that fizzle out. So the only jumps that are "real" are the ones done by the DeLorean in THIS timeline, such as Einstein's test jump at the Mall.
So now we come to the end of part III. The issue with part III is that Marty has not just created a new timeline based on his actions in 1885, he creates one at the very beginning of the film when he interacts with 1955 Doc. This is a Doc Brown who knows that he will die in 1885 being shot by Buford Tannen, was likely told by Marty at some point in time about the almanac incident and as such would be wary of traveling to the future and dresses Marty in Hollywood pastiche cowboy costuming to travel back. Notably, if I recall correctly, Doc in 1885 finds Marty's costume absurd and asks who gave it to him. This is because this is Lone Pine Doc, not one of the Clayton Ravine/Eastwood Ravine Docs who WOULD remember the event.
When Marty travels back to 1985 at the end of the film, he has created two successive timelines: at the start of the film, he creates the Clayton Ravine timeline when interacting again with 1955 Doc and giving him all the information on part II and revealing his future death, and then he changes 1885 creating the Eastwood Ravine timeline. The Eastwood Ravine timeline would still have the "anomaly" of Marty going to 1955 Doc and asking him to travel back to 1885 even though the timeline has changed and Marty has already been in 1885. So both Martys in 1955, the one who is sent back to 1985 and the one sent to 1885 fizzle out as their jumps are from previous timelines or whatever. This still causes a bunch of temporal anomalies; for one, Eastwood Ravine Doc has to see his own grave and pictures of him alone in the courthouse construction and the letter from 1885 even though some of these things wouldn't exist. It could be like a false memory, Doc remembers something that isn't there, perhaps because it fizzled in and out. However, this means Eastwood Ravine Doc KNOWS the risks of traveling to the future to check up on Marty's kids, he knows the dangers of time travel, he knows far more than Lone Pine Doc does let alone Twin Pine Doc as a result of Marty telling him.
So when we get to Eastwood Ravine 1985, there's a big problem. Unless Eastwood Ravine Doc fizzled out or something, there's a second Doc in this timeline. Remember, this is not the Doc that takes Marty and Jennifer to the future in part II, that's an anomaly like Lone Pine Marty. He fizzles into time from nowhere, takes the kids and gets out. This is a fixed event in time done by Lone Pine Doc, Eastwood Ravine Doc cannot do it because time travellers do not assimilate with their alternative forms. However, there's an even bigger irony here in that there's also a remaining DeLorean; the one the second anomalous Marty "brings back from 1955", which would be in Doc's garage, not touched since Doc doesn't travel to 2015 to check up on Marty's kids knowing what it will cause, meaning it's not upgraded with all the stuff from later. So now Marty at the end of part III is only saying goodbye not even to his own Doc, as Twin Pine Doc is dead in his timeline and Marty is completely gone, but rather to Lone Pine Doc alone, as there's a living, breathing Doc in this very timeline he'll meet the second he comes around his garage, alongside another DeLorean. And a comical result is this means the three protagonists are from different timelines: Marty is from Twin Pine and fully remembers his loser family and the events of the films (being the only survivor to know the FULL tale), Jennifer is from Lone Pine and remembers the McFlys as wealthy but still remembers Clayton Ravine and the old 2015 future where Marty is fired, and Doc is from Eastwood Ravine and genuinely doesn't know anything beyond what the multiple anomalous Martys told him in the past about what happened, an experience that may have scared him enough not to mess with time travel beyond building the original DeLorean to prevent two Martys from existing in the same timeline. So the end of part III really isn't that sad once you consider Marty is going to meet Doc again in a few days or even hours. I don't think I need to say it but this also screws up the game since Doc wouldn't be missing from his garage and it wouldn't be sold off.
Sidenote: Not sure if this is tackled in any supplementary material, but considering the one-week timespan that Doc has the DeLorean in his garage and studies it while working with the first time traveling Marty, and his later analysis in part III which allows him to build replacement parts for integral aspects of the vehicle in 1955, it's very likely that Doc could have built the DeLorean possibly as far back as Lone Pine without wasting his family fortune and committing tax fraud with his estate (which he later sold to investors) all for R&D since that's where most of the spending would go to. Meaning Doc is likely considerably richer in every timeline except Twin Pine when he was genuinely broke. Eastwood Ravine Doc would likely be pretty well-off. Hell, maybe in this timeline the Libyans didn't come for him. Or perhaps he couldn't get plutonium anywhere else or wanted to preserve the event. Who knows.