I like this idea of Tim figuring out Peter is Spidey.
(if it's in a universe where Peter lives in Gotham) them meeting in school and knowing eachother but then Robin and Spidey meet afterwards and they're both like "waaaaaiiiit a minute"
Peter is VERY intrigued by Batman's tech and reverse engineers it.
Tim is obsessed with his Web Shooters and makes his own, he never uses them but he has them at the ready.
When they're on patrol Tim carries extra Web fluid for him.
Peter introduced Tim to Star Wars and they have "lightsaber" fights, Peter almost always loses because of Tim's experience with a Bo Staff
Both of them are falling asleep literally everywhere, they always find the other and just stay with them.
they like to patrol together because it's like the only time they get to spend together but it creates WAY too many arguments from them both being overprotective.
they share random facts and theories, (mainly science and movie facts and theories)
they're texts consist of sending memes and saying "I wish you were here, I'm so bored" "look outside" and then boom they're there.
They both take tons of photos of eachother, they have them pinned or taped to their bedroom walls.
they have a shared playlist, they share Pete's Wired earbuds all the time.