In Back to the Future Part III, when Doc accidentally brings up Marty's future car accident, which had not yet happened to Marty, Marty asks what accident and Doc decides not to say on grounds that he shouldn't know too much about his own future, Marty asks "what is wrong with my future?", almost like he was aware of his future being bad.
Now he kinda was. When he saw Biff in 2015, and Biff thought he was Marty Jr., he's surprised to learn from Biff that he will become a loser, though he's not given much time to think about this before Griff comes in. And it doesn't seem to be on Marty's mind throughout the adventure, but could he have suddenly remembered what Biff told him (maybe he could have said "the Biff of 2015 told me there was something wrong with my future")? Or could it have been a combination of this and the few times in 2015 when Doc tells Marty he shouldn't know too much about his future when Marty asks how he turns out, perhaps Marty sensing Doc's not telling him on grounds that it's too bad - even though the Doc of 1955 had already told Marty they shouldn't know too much about their own futures? Heck, could Marty have actually noticed Doc's brief double-take in 1985 before telling Marty that he and Jennifer will turn out fine?
It's also interesting, Doc seems to be concerned about people knowing too much about the future, and keeps Marty's car accident/bad future a secret from him, and he doesn't want him to know things like future sports scores, but these things had not happened to them yet - the future could change, but when continuing from their 1985 present, things won't be confusing. And also, Doc took Marty to the future to prevent his future son from going to jail, is that any different from warning him about a car accident?
And when Jennifer tells Doc that the paper she got from the future erased, Doc's just happy about the future not being written yet, unconcerned about future changes. Doc isn't told what was on the paper nor was he told that Marty avoided the car accident (unless Doc had known the exact time of the accident and went to 1985 after that time - though it would have made more sense to travel there a few seconds after Marty's return - he had no way of knowing that Marty would be there when he showed up).*
And that's ignoring the fact that 1955 Doc learns a bit more about 1985 Doc's future fate. Marty tells 1955 Doc about why he's back there, briefly mentioning getting a book from Biff (but I feel that's easy to forget, and he's not that detailed), after they see Doc's headstone (which Marty probably should have just avoided telling the 1955 Doc - it would have made more sense for him to want to rescue Doc without telling him, and would explain why that Doc is surprised when Marty comes back for him), and Doc does seem to be a little careless in 1885. It's one thing before Marty comes back for him, when it looks like he won't be returning to 1985 (any alternate reality he creates from his time in 1885 won't affect him because he won't be back and confused, though Marty could be confused by the changes), but after Marty comes back and Doc expects to return, they do things like rescue Clara (don't they remember Marty endangering his life by saving his dad?) and don't care much about the train crashing (though this would be out of necessity for them).
*And this is ignoring the comic books, which reveal that Doc's trip to 1985 at the end of part III was not his first trip to the future after being in 1885, and had some interaction with Marty before Doc went to that point in time, so that Doc would have known Marty's future will be better.