Will Smith had success as a rapper, and he’s developed a pretty efficient rhythm in his movies too, alternating a big, usually mediocre, action picture with a sentimental heart-tugger. After “Hancock,” it’s sentiment time, and so he offers “Seven Pounds,” an incredibly sappy and manipulative dirge disguised as a deep rumination on sacrifice and redemption. Even for the tearjerker it wants to be, Smith’s second effort with director Gabriele Muccino (“The Pursuit of Happyness”) is an extraordinarily outlandish affair.

This is one of those movies that wants to keep you in suspense about what’s happening before springing a big surprise at the close, so it would be unfair to reveal too much about the plot. But it’s certainly okay to sketch the premise. Ben Thomas (Will Smith) is an IRS agent who contacts a number of people whom he claims to be auditing—who seem to have nothing in common apart from the fact that all suffer from some physical malady or face an imminent danger. The most important are an abused wife (Elpidia Carrillo) and Emily Posa (Rosario Dawson), a young woman afflicted with congestive heart failure. He also has a curious phone conversation with a blind man, Ezra Turner (Woody Harrelson), who works as a customer service operator for a meat-by-mail operation.

But Ben’s one curious treasury man, a sad, sensitive fellow so solicitous of those he’s investigating that he gets involved in their lives. That’s particularly true of Emily, whom he helps so much that she begins to fear he might be stalking her. But it’s inevitable that they should eventually develop feelings for each other.

Still, it’s unclear exactly who Thomas is. For a government worker, he’s oddly transient, taking up residence in a fleabag motel. He has occasional conversations with a sad-faced guy (Barry Pepper) who seems upset to see him. He speaks by phone with his brother (Michael Ealy), who’s obviously concerned about him. Is he some sort of con-man? Or a guardian angel trying to win his wings? A rogue agent? And what’s with that circular aquarium he keeps in his dingy room, which houses a dangerous jellyfish?

Writer Grant Nieporte strives desperately to keep you in doubt about Ben’s identity and motivation for the greater part of the movie, but brief flashbacks indicate that he had a very different life in the past, and Smith’s performance makes it clear that he’s a stricken individual consumed by psychological pain. And given Thomas’ interest in discerning whether his subjects are good people—a rather unusual goal for an IRS agent—an observant viewer will begin to suspect what he’s up to long before the picture reveals his secret. Any viewer who’s not an absolute sucker for emotional manipulation, moreover, will probably be appalled by the mechanics by which the plot is resolved—and which raise troubling moral issues that picture doesn’t bother to address at all.

But setting aside all that, it’s hard to see “Seven Pounds” having the uplifting effect on audiences that it’s obviously aiming for. It’s an almost unremittingly dark, gloomy piece, apart from a few bits involving a snide motel manager (Joseph A. Nunez). And Smith suffers so grandly throughout that the whole thing takes on a soap-operatic effect: by the time you reach the last act, you might be forgiven for thinking the subtitle should be “The Passion of Ben Thomas.” Dawson, by contrast, makes a likable romantic interest, and the steamy bedroom scene she has with Smith is effective enough (though it must be said that such vigorous physical activity seems unwise for a woman like Emily, who’s recently fainted just from the effort to walk her dog). The rest of the cast is basically window dressing apart from Harrelson, who gets a rare opportunity to play beatific rather than down-home scoundrel. The droopy atmosphere is accentuated by the washed-out widescreen images offered by Philippe Le Sourd, who emphasizes shadowy grays and blues while taking special advantage of the sequences set in rainstorms. Angelo Milli’s moody, insistent score fits the visuals and the melodrama, which isn’t exactly a compliment.

Even the title of “Seven Pounds” is enigmatic, but in the end the movie is a puzzle not worth solving.