Tony after finding out about this Spider-Man, ends up basically taking him under his wing from the moment he meets him. His care for Peter is seen from their first scene together and it only gradually grows. With them spending more time, the internship Peter gets at Stark Industries and the way he gets taken under Tony's superhero mentorship. In Spider-Man: Homecoming, the moments where they argue and Peter gets benched show how much Tony really cares for the kid's safety and how he wants him to stay away from all this mess. But, alas, that wasn't ever in the cards for Peter, so he ends up actually guiding him. In Avengers: Infinity War, we see how heartbroken and sad Tony gets seeing Peter vanish and in Avnegers: Endgame, at the start when he comes back to Earth, he says how he couldn't save the kid. During the movie, when the other Avengers come to ask him to help figure out a way to travel in time to stop Thanos, he refuses because of the life he's built for himself in those years. But, not too long after he spends time and figures out a way, because of his regret in not being able to save Peter and the half of the world that got dusted. His hero complex and his bleeding heart can't help but do this for them. When he finally sees Peter in the battlefield, he just pulls him in for a strong hug, looking so relieved and happy that the kid was back. We know that they had a special bond, due to the kind of person Tony was because of the life he lived and the kid Peter is without a father or a father figure in his life. Their moments were truly heartwarming to see. The way that Tony makes upgrades and builds a whole new suits for Peter and how he leaves him with the E.D.I.T.H glasses, leaving most of his work for him is just more proof for the love and care he had for the kid.