There’s the kind of bad movie that just sits there, unfolding with grimly predictable monotony. Then there’s the kind where the badness expands and metastasizes, taking on a jaw-dropping life of its own, pushing through to ever-higher levels of garishness. “The Book of Henry,” directed by Colin Trevorrow from Gregg Hurwitz’s script, is of the latter, you’ve-got-to-see-it-to-disbelieve-it variety.

The film’s muted yet still rather flamboyant terribleness derives from the fact that it seems to be juggling three or four borderline schlock genres at once. It starts off as one of those movies about a precocious kid genius — and on that score, for half an hour or so, it’s actually rather watchable. Then it evolves into a tale of the child abuser next door. Then it morphs into a disease-of-the-week weeper, at which point the awfulness is only just getting started. For “The Book of Henry” — I’m trying not to give too much away — is a movie about how an 11-year-old brainiac lays a trap for the child abuser, all as a way of taking everyone through the grieving process. It’s not entirely clear whether you should be laughing, crying, or waving a white flag.

In the picture-postcard town of Cavalry, New York, Henry Carpenter (Jaeden Lieberher) lives with his feisty, affectionate, video-game-playing single mom, Susan (Naomi Watts), and his little brother, Peter (Jacob Tremblay), and he knows everything about everything. He knows how to play the stock market (and win!), which is why he handles the family finances. He knows advanced mathematics and medical science and how to build Rube Goldberg contraptions in his treehouse — and more than that, he knows how to feel and express things with adult emotion. He’s not one of those Hollywood whiz kids whose head is bigger than his heart. He’s a genius of humanity as well!

Jaeden Lieberher is the best thing in the movie. As Henry, he never smiles, but he’s sly and quizzical and engaged, with a look of woodland-animal alertness that reminded me of the young Leonardo DiCaprio (remember him in “This Boy’s Life”?). When Henry, using his binoculars and his intuition, figures out that Christina (Maddie Ziegler), the sweet but shy girl next door who is one of his sixth-grade classmates, is undergoing something terrible at the hands of her police-inspector stepfather, a real get-your-leaves-off-my-lawn type named Glenn Sickleman (Dean Norris), he’s compelled to become her savior.

But then that pesky illness gets in the way. All the objections one might raise to a movie that features a tragic ailment crashing in out of nowhere are at play here: that it’s a way of manipulating the audience, of programming our responses rather than earning them. Trevorrow, who made “Safety Not Guaranteed” and the highly impersonal stomp machine “Jurassic World” (he’s also set to be the director of “Star Wars: Episode IX”), knows a thing or two about programming responses, though he isn’t bad with actors. He draws out Sarah Silverman as Susan’s snippy boozer waitress pal, and Watts lets her feelings shine right through her skin. The actress doesn’t hit a false note — at least, not until the disease drama gets put on hold. But it’s here that “The Book of Henry” enters a zone of domesticated preposterousness.

At this point, we’re asked to believe that Henry is such a genius that he can see and anticipate … anything. He can hold an entire conversation in advance (he’ll know just what you’re going to ask, and just when you’re going to swear). The picture veers slowly and steadily into kitsch, especially during the sequence when it crosscuts between a grade-school talent show and an attempt to vanquish Glenn with a little old-fashioned justice purchased at a gun shop. We’re supposed to be glimpsing the tale’s grand design, but what we see, for the first time, is that the entire thing is a crock: a film dreamed up by people who are moving “human situations” around like pieces on a checkerboard.