i'm totally back in my irondad phase right now so here are some of my favorite head cannons!!!
they both have stupid names and contact pictures for each other. Peter was mortified when Tony found out, until the man himself casually switched his name from "Peter P." to something stupid like bug boy. and now they're constantly updating each other's contact to whatever relevant bit they have going on
Peter tries (and fails) to teach Tony all the current pop culture and media references, and Tony tries (and succeeds) to teach Peter the classic films and rock bands. the result is a Black Sabbath obsessed Peter and a Tony who embarrasses him by purposefully miss-using trending lingo ("clock in" "mister stark, its clock IT" "tomato, tamato")
they get each other the way most people don't. losing their parents, super-geniuses, super-heroes, bad self-preservation skills. they help each other heal in a lot of ways and they don't even realize
Tony has a wide array of nicknames for Peter. Kid, kiddo, Spidey, webs, buddy, squirt, etc. Peter's catalog of nicknames for Tony consists of "Mr. Stark" and, on some very rare occurrences, "Tony" he's called him Anthony once, when he was pissed off, and Tony was so taken aback he was for once in his life speechless
seeing Peter hurt scares Tony beyond belief, so he always attempts to lighten the kids mood and joke around. seeing Tony hurt reminds Peter of uncle ben and his parents, so its one of the few times where he is 100% stone cold serious
they have countless inside jokes that have stemmed from too many late nights in the lab and long missions. sometimes its like they're speaking their own language, so everyone else just gives up on trying to make sense of it
Tony gave up drinking after Civil War. the only reason he never relapsed or even considered picking up the bottle again is because of the kid. not only does he want to be a better role model, but he is terrified of becoming his own father, of messing up what they have
Peter is the reason Tony and pepper ultimately decided to have Morgan. he showed him how capable he could be as a father and how much he wanted to be a dad
Peter refuses to let Tony replace is worn down or broken things, so the man just slips them in when he can. "hey kid, you want this hoodie? its a bit small on me." "SI is doing a partnership with some watch brand, we got some lying around. Why don't you take one home?" "Im thinking of adding some stuff to my phone in the lab. you want an upgrade, Webs?" Peter catches on after a while, but never protests. he's learned that this is one of the ways that Tony shows he cares, so he accepts it and is grateful
sorry this is so long, I just love them and miss them so much ugh. please give your own head cannons or thoughts if you like!!