A droll, understated, appealing coming-of-age tale about an overweight high school misfit who’s befriended by an odd but committed principal and develops a bond with a couple of other outsider classmates, “Terri,” like its titular protagonist, lumbers along, and some viewers will find it painfully slow. But the deliberation is actually part of the charm of Azazel Jacobs’ offbeat picture, which will certainly grow on you if you give it the chance.

The secret of the film, written by Patrick deWitt, is that it treats all its major characters, however peculiar they might initially seem, with affection, never turning them into easy punchlines. And they’re all played with unforced naturalness by the cast. Jacob Wysocki is a revelation as Terri, a bulky teen, long abandoned by his parents, who lives in a cluttered, out-of-the-way house with the troubled uncle he tends to (Creed Bratton of “The Office,” who shows he’s no one-trick pony). Terri goes to school in pajamas and is routinely teased by most of his classmates, but his response is resignation rather than retaliation.

Terri’s noticed by the school’s vice-principal Mr. Fitzgerald (John C. Reilly), a voluble fellow who makes a point of taking those he perceives as “special” students under his wing via once-a-week counseling sessions. He’s an unconventional fellow whose methods veer from calculated rants to avuncular prodding, and Reilly skillfully catches his every facet, making the character engaging without allowing him to become a joke.

In the course of his meetings with Fitzgerald, Terri meets another of the principal’s targets, scraggly, foul-mouthed Chad (Bridger Zadina), a snide, mournful troublemaker who constantly pulls at his hair and shows up unexpectedly at Terri’s ramshackle house for a chat. And Terri witnesses an in-class sexual encounter between a would-be stud and pretty but easy Heather (Olivia Crocicchia), and is instrumental in persuading Fitzgerald not to expel her. Before long she and Terri have a sort-of date, which Chad intrudes on; that leads to a long night of drinking and conversation that might be thought of as a less synthetic version of “The Breakfast Club,” in which Zadina and Crocicchia match Wysocki beat for beat.

The film blends episodes that mingle pathos and humor—Terri’s forced introduction to the world of mouse-catching, or the funeral of Fitzgerald’s long-time secretary, to which Terri and Chad insist on accompanying the principal. But in each case deWitt, Jacobs and their cast avoid the expected and tease out layers and shading that make the sequences feel fresh and, despite the slowness with which they’re told, oddly invigorating. This is a scenario that, in the wrong hands, could have descended to the level of a crass, mindless, utterly superficial Hollywood high-school comedy. That it doesn’t is a tribute to all involved.

“Terri” is, of course, a small independent film, and technically it’s not slick. But Tobias Datum’s cinematography is evocative without sacrificing authenticity, and Mandy Hoffman contributes a background score that enhances the mood without overwhelming it. The result is a rare find, a film that demands patience but rewards it as well.