Sirius and Remus were touchy and affectionate with each other even before realising they had feelings for each other. Just like friends.
Nobody questioned them because that's how they were.
They did things like fixing each other's hair without asking, squeezing their chin or jaw as a way of affection, kissing each other's cheeks, touching hands like playing with each other's fingers or bracelets or rings. Like leaning closer when they sat together and putting their head on the other's shoulder. Like bumping hips in a playful way when they brush their teeth together. Like borrowing each other's clothes without asking because they liked each other's smell. Like "accidentally" falling asleep in each other's arms after a late night studying.
It was such a natural thing for them.
Sirius would pull Remus's arm while they were in class, roll his sleeve up without asking and start drawing beautiful things there. Remus would hate washing them off in the shower. Remus would carry hair ties and combs for Sirius's hair and hand them to him when he felt Sirius kept pushing it back when it was on his way. Sirius would save Remus sweets he was given for example for Valentine's day because he wasn't much of a sweet tooth like Remus was and he loved the way he beamed with a piece of chocolate. Sirius would lay his head on Remus's lap whenever he wanted and Remus would immediately know Sirius would want his fingers running through his hair. Plus Remus is the only one that can touch his hair.
Remus and Sirius were orbiting towards each other for a long time as if their bodies and natural instinct knew they loved each other even before their minds could process it.
Even though those stupid minds were stubborn to think their love wasn't reciprocated. That's why they took a long time to confess their feelings.
Once they started dating nothing changed much between them. Except for kisses, sex and more intentional touches.