How old is the platy? It's possible it could simply be a symptom of old age. [I get the impression that 3-ish is considered the current life expectancy of a platy.]
Is it eating enough? The curved shape you describe actually seems less evident to me than the flatness of the belly.
How is your water quality - ammonia, nitrite, nitrates in particular? Ensuring that they are at 0, 0, <20 (or <20 above tap water levels) at all times is crucial. As for water parameters, platies are generally hard water fish, so, if your water were soft, that might account for the problem.
I've had a lot of fish which have developed spinal problems in the past couple of years - curvatures when viewed from above or laterally, to the extent that the tail almost seems to 'break' ultimately before the fish's final demise, and also becoming increasingly emaciated. Coincidental or otherwise, I also had a young shoal of fish, many of whom developed spinal curvatures similar to the arch shape you describe before dying very prematurely. Whether or not the older fishes' problems were old age, TB (mycobacteria marinum which they'd be more susceptible to due to being old - and possibly brought in by the newer shoal of fish which may have been carrying it) or something else altogether is unknown - only a post-mortem would be able to definitively prove/disprove TB. I sought advice from a well-renowned expert recently and asked this specific question about TB - they pointed out that not all fish display symptoms or necessarily all the symptoms, so equally I wouldn't rule it out.
Whatever the cause is is probably neither here nor there - I would continue giving the same care/attention as usual. However, just in case it is TB, then I'd take extra care when doing tank maintenance to ensure no open cuts on your hands through which an infection may transmit - either postpone the tank maintenance until it's healed or wear gloves (although I've never succeeded yet in not ending up with water entering the gloves!). If you have a spare tank (and heater if you use one and filter), then that would be an added layer or protection for the fish - you could isolate this fish and any others displaying symptoms and keep them in it separately to avoid any further cross-infection; while most of the fish I mention have died in recent months, I continue to house one on his own in the spare tank and he's faring well (while the others are protected in the main tank).
Hope that helps.