Peter didn't start as the tagalong. He just wanted someone to reach out to, and there was James, Sirius, and Remus. It wasn't until some years later, between third and fourth year, that it really became obvious. By then, the Marauders had been named, getting up to all sorts of trouble.
Truthfully, it wasn't until they gained their Animagus forms (just toward the end of fourth year), that Peter felt any sort of security in his place with Hogwarts' biggest trouble makers.
That was when he started to calm down.
And so the transformation began in earnest. James and Sirius, picking up on the fact that no one took Peter seriously (and never would, what with only three years in school remaining), began to work toward building up Peter's confidence.
The boy had always been somewhat shrewd to begin with—he wasn't a complete lump, after all. He picked up on James' and Sirius' coaching, and what began as the Marauders fanboy shifted into their grandest masterstroke.
Peter Pettigrew, the trembling lump, could get past anyone with the illusion of incompetence and inadequacy. And once their guard was down, the Marauders could go in for the kill. He was an actor, and that was something James and Sirius had no issue taking advantage of. At first, Peter reveled in his evolved role. Later, though, as they begin to wrap up their time at Hogwarts, Peter would confide to Remus he felt he was being used.
Remus said he was reading too deep into it, despite his own misgivings on the subject.
(Funny, how it all turned out to be their undoing.)