Is it possible for a movie to be at once ludicrously silly and genuinely moving? That’s the strange question you might find yourself asking while watching “The Age of Adaline,” a romantic fantasy with surprising heft that will likely have you scoffing at one moment, then furtively wiping away a tear the next.

It’ll also have you marveling at the emotional resonance that a seasoned pro like Harrison Ford, Ellen Burstyn or Kathy Baker can bring to a supporting turn. Ford, in particular, takes what could have been a solid but unspectacular role and turns it into the film’s highlight — and perhaps one of his better performances in years.

It’s no accident that the poignancy of Ford’s performance comes from his evocation, as a middle-aged father, of both the pleasure and pain that aging brings — both the well-earned wisdom and the inevitable regrets. The entire film, directed by Lee Toland Krieger, is about age and our common assumption that younger is always better. Not so fast, the film is telling us. Smooth, unwrinkled skin and ungraying hair isn’t everything.

Of course, when that skin and hair belongs to gorgeous Blake Lively, it’s not easy to have much sympathy at first. Lively grows on you gradually in the role of Adaline, a young woman with a big secret. We first meet her as she’s arranging for a new identity, fake passports and all. Back in her apartment, we see hints that she’s not all she seems: fraying, sepia photographs, or a dusty old manual typewriter.

Turns out that Adaline, though we’re in the present time, was born in 1908. She married, had a daughter, lost her husband and then, at 29, almost drowned when a car accident landed her in frigid waters. Somehow, a scientific process involving a bolt of lightning both revived her heart and, yes, stopped her from aging.

Looking like a young Blake Lively forever might not seem much of a problem. But it’s a lonely existence, because once she hits 45 or so, Adaline arouses suspicion. She has to basically live on the run, changing identities every decade. She also can’t live with her daughter, who’s aging normally, which means she can only live with her dog — or succession of dogs, since each will die, sadly, at a normal rate.

Then one day, Adaline meets a handsome, soulful young entrepreneur (Michiel Huisman, of “Game of Thrones”). She tries to resist his advances, but he won’t take “no” for an answer. And when he asks her to accompany him on a visit to his parents (Ford and Baker) for a weekend, she finds herself accepting. It is here, because of a plot twist that would be unfair to reveal, that things get really, really complicated.

Lively is appealing, natural and often touching. Unsurprisingly, she rocks the vintage fashions. And she makes a game effort to appear timeless. The actress’ handicap here, though, is that her natural delivery reflects her extremely contemporary presence — making her sound stiff and a bit forced when she utters a phrase like “picture houses” instead of movie theaters.

But she has nice chemistry with Huisman, and there’s a moving quality to her scenes with Burstyn, who, as her daughter, is reliably pitch-perfect and brings a sense of groundedness to the fantastical premise.

As for Ford, he, too, must ground an intentionally fantastical story, and the way he does it is the most compelling part of the film. (Baker, too, is quite touching in a smaller role.) Even if you laugh in the beginning, you likely won’t find yourself laughing at the end, thanks to the veteran actors in this film.

See? Getting older really does have its virtues.