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Sandra Bullock, left, and Melissa McCarthy play mismatched cops chasing a drug dealer in South Boston.

Ho-hum, you got the earnest, straight-laced, by-the-book cop, which surely means you must also have the loose-cannon, foul-mouthed, off-the-wall cop. Do the math and, if this were funny, The Heat would add up to your average buddy-cop comedy. Except that it's not funny, at least not very and not often. So that's one difference. Another is that the mismatched buds are females this time – Sandra Bullock, slim in her neat grey suit, and Melissa McCarthy, less slim in her sloppy grey sweats. Bonus points for guessing who plays which cop.

McCarthy is reunited with director Paul Feig of Bridesmaids fame, also a girl bonding flick but ranking considerably higher on the laugh-meter. So what's the trouble on this go-round? Well, at the risk of seeming untactful, weight is definitely an issue: The script has blimped up to a running time of nearly two hours, a corpulence that's never a good sign in the comedy biz. Humour almost invariably needs a leaner, faster profile. By contrast, this thing dawdles and meanders and lacks any sense of pacing. The lines have no punch; at best, they paw. Worse, much of the scripted flab can be blamed on sheer repetition – a one-note conceit huffing and puffing and puffing and huffing until the joke gets really tired. That's about 10 minutes in, and there are miles to go before it sleeps. Happily, we aren't similarly constrained.

The milieu is South Boston, where Bullock's Sarah is the interloper, a stern FBI agent possessed of lacquered hair, a poker up her butt, a career without flaws and a life without friends. Raised in foster homes and over-compensating ever since, she lives alone with a cat – actually, her neighbour's cat. Of course, charged with the task of removing said poker from said butt is McCarthy's Shannon, who patrols a beat in her deadbeat duds. Before her constant barrage of four-letter words, two-legged perps crumble like stale cookies in the bargain bin. Her many amorous conquests do likewise, regularly popping up to beg for another ample roll in the hay. Self-assured, sexually accomplished, the quickest of first-responders, she's a one-woman Boston Strong. Which is where the picture goes badly wrong with McCarthy, but more about that later.

In the meantime, obliged to team together in quest of some drug kingpin or other, the pair mosey along from inflated set-piece to inflated set-piece. The bickering arrives early, tailor-made for the fairer sex. One cop points: "Your breast is invading my space." The other retorts: "Keep your finger off of my areola." Then comes the repetition, like the redundant interrogation-room scenes. One cop applies psychology straight from the Agency handbook; the other applies her gun straight to the suspect's crotch. The colloquy continues on the dance floor of antic clubs, on the beer-stained stools of seedy bars, in speeding cars and in the villain's den, until Ms. Straight-Lace learns to unbutton (literally) and to admit to her vulnerabilities.

Which brings us back to the picture's problem. It's not just that the principals, gifted comedians both, are working without any consistently amusing dialogue – screen history is strewn with gifted comedians expected to labour under that tiny handicap. Instead, they're cast in the wrong roles here. It would have been much funnier, and richer, to reverse the characters – slim plays loose-cannon confidence, less slim plays by-the-book insecurities. Why? Because McCarthy's over-sized persona requires what Bullock doesn't – an element of vulnerability to bring our her full comedic potential. Bridesmaids gave her a little, and Identify Thief enough that, in a brief yet memorable sequence, she got to dig beneath her trademark mania to show off some seriously good acting chops.

Girth and comedy are worthy companions and a fascinating topic, a buddy story in itself. Many men – Fields, Hardy, Gleason, Candy – have combined the two, but few women. To her great credit, McCarthy does so with such assurance that her size becomes the benign elephant in the room – rarely spoken of and certainly conquered but still very much there, an essential component of her comic shtick. Essential, because she's at her funniest when the courage of that conquest is there too, when the sense of frailties confronted and forces overcome is also part of the shtick. This is a tepid comedy for many reasons, but not least for depriving Melissa McCarthy of her vulnerability and thus of her courage – that is, The Heat takes from a hilarious woman precisely what makes her so tantalizingly hot.

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