I think this might be the smallest change from the book with the most profound impact. I've thought about it for a while, and since the movie finally got a full home release today, I want to take a minute to unpack it.
It's just one line, it's as small of a change as it gets, but if you really think about it in the context the story's themes and worldbuilding, the implications are tremendous.
The difference between "I can give, I have extra" and "I can give, I go home six years slower" is that the former, while still a great act of kindness, is ultimately no skin off Rocky's back, whereas the latter involves Rocky actively going against his own self-interest. Obviously being alone in space sucks, but more importantly, it's dangerous - any additional time spent in it is necessarily going to lower the mission's overall chance of success. It's impossible to put a number on it, and it isn't big enough to not be worth it as far as Rocky is concerned, but it's not zero.
You could make the argument that, at least on a philosophical level, this is an even more significant sacrifice on Rocky's part than breaking into the Hail Mary's atmosphere to save Grace's life, because at least that was still actively beneficial to the mission. Obviously it was just as much, if not more, for the sake of his friend as it was for the mission as a whole, but it still was for the mission as a whole: "Save Earth. Save Erid." The director's commentary even confirms that the little xenonite figures Rocky left that tell Grace how to open the sample probe was his way of firmly saying "Finish the job."
Compare that to this scene, where, if only on a very small and abstract level, Rocky is saying "To hell with me and the mission - your life is more important."
This is very significant, because up until that point in the story, Grace and Rocky's friendship has been built on mutual self-interest - "live together, die alone". This doesn't make it less good or important, to be clear, but it's not at all unexpected. If you're a conscious, rational animal like a human or Eridian, it makes perfect sense to do that, and even if you're not, you're very likely to evolve the instinct to do it anyway.
The instinct to cooperate under mutually-beneficial circumstances is overwhelmingly common in nature and found in animals at every level of complexity, and it's so common to see it cross the species barrier that we have a name for it: symbiosis. However ruthless and brutal evolution tends to me, it usually makes more mathematical sense to be nice and cooperate with each other than to be an anti-social jerk.
Self-sacrifice, on the other hand, a willingness to actively go against your own self-interests for the sake of another living thing, is far more rare. Evolution is fundamentally a numbers game, and anything that lowers your chances of surviving to see another day and pass on your genes, however small, is going to be selected against. This is why most animals fall back on "every man for himself" when backed into a corner, even when their own offspring are involved - living to see more mating seasons is going to result in more genes being passed down in the long run than sacrificing yourself for one litter that won't survive without you anyway. It seems terrible to us, but it makes sense for an animal who isn't consciously considering anything they do and is just following instinctual urges honed by evolution.
So how do self-sacrificing instincts evolve, however rarely? By having a species become so social and cooperative, so intrinsically dependent on one another, that they start evolving and interacting with evolutionary pressure more often as collective groups than any one member does as an individual. A wolf willing to sacrifice itself for its pack is less likely to survive and pass on its genes, but a pack of wolves made up of members who are all willing to sacrifice themselves is more likely to survive than a pack whose members are only out for themselves, and over millions of years, the latter wins out over the former. And this is exactly what ended up happening with us.
Now, obviously, not all people are good. There's still a lot of selfishness in the world, but the fact that humans are willing to self-sacrifice at all, let alone as often as we do, is very evolutionarily significant, and a testament to how much being social and cooperative has molded the way we evolved. When you really think about it, on small levels, we act against our own self interest for others all the time - we wait to let people cross the street, we cover lunches and snacks and groceries for our friends, we sacrifice time and effort to talk to people if they need help or support, and so forth. We're more likely to do it for people we know, but we still do it for strangers constantly, and we often see it as an essential part of "what makes us human".
There's even a whole quote from The Martian about this: “If a hiker gets lost in the mountains, people will coordinate a search. If a train crashes, people will line up to give blood. If an earthquake levels a city, people all over the world will send emergency supplies. This is so fundamentally human that it's found in every culture without exception. Yes, there are assholes who just don't care, but they're massively outnumbered by the people who do.”
So we see, in this scene, it isn't just fundamentally human - it's fundamental to people. Any species that evolves to the point of being rational and conscious is necessarily going to be social enough to evolve these exact same traits, no matter what biosphere they do it in.
And the really neat thing is that this point is brought up in the book, very explicitly, but in a different scene that didn't make it into the movie. During some downtime, Grace and Rocky have a whole conversation where they talk about the traits they convergently evolved which made it possible for them to meet and communicate. They bring up the merits of self-sacrifice from an evolutionary point of view, and conclude that even though plenty of selfish humans and Eridians exist, it makes sense that they both evolved an instinct to be selfless at least sometimes because they both had to occupy the same evolutionary niche to evolve rational thought: cooperative, social, tight-knit pack hunters.
The filmmakers took a scene from the book that (I'm guessing) would have been difficult to work into the script and did some lateral restructuring, working the idea into the fabric of the story itself. It's much harder to consciously notice, but it's still just as impactful, if not more.
