The whole youthful and innocent vs older and sexy thing actually gets brought up at the end of the first book.
Cinna puts Katniss in a dress that is consciously designed to make her look much younger than she actually is, so as to play up the ‘teens in love’ angle they’re trying to sell the Capitol.
But the dress also has padding, so as to make her breasts and hips seem larger than they are, since she’s been literally on the verge of starvation for weeks, and wasn’t eating that much before that, and as a result she isn’t that curvy. Katniss is shocked by this, but Cinna explains that the dress was actually a compromise, because the original Capitol plan had been to give her plastic surgery.
Katniss then realises that none of the male tributes grew facial hair in the arena, even though several of them were old enough (note: she doesn’t say that all of them were old enough. Though Rue was the youngest, this suggests that there were other tributes who were young teenagers) and that something must have been done to them to prevent that from happening.
Also, it’s worth considering that Katniss and Peeta probably looked even younger than your typical sixteen year olds.
Katniss makes a big deal about how much they both get to eat at home, but if you read between the lines, Peeta lives off stale bread from the bakery and the odd bit of meat, and Katniss is essentially living the hunter gatherer lifestyle, supplemented by what they can buy from the baker and what they can get from Prim’s goat.
They’re much more well-nourished than the bulk of District Twelve, but Katniss can still easily spot the Career Tributes, because they’re the ones who have always had enough to eat. She’s one of the older (and therefore almost certainly heavier) tributes, but she still gets to hide in trees to get away from the Careers, because she’s significantly lighter than all of them.
Malnutrition tends to push back puberty. Katniss would probably be less well-developed than a modern teenager of the same age.
Notably, we don’t hear about her getting her period— or even wondering about that like she does with the facial hair— in the arena. Which, yeah, could be because of our culture’s habit of viewing menstruation as less kid-friendly than graphic child murder and mentions of prostitution, but it’s worth considering that in real life she might well have not started it yet.
While wearing the final interview dress, even with the padding to give her bigger breasts and wider hips, she says she looks about “fourteen at most”, which even accounting for Cinna’s borderline magical design skills, suggests that she probably tends to look like a younger teen even without it.
The Hunger Games would have been almost unbearably disturbing, if they hadn’t decided to cast almost all the characters as incredibly fit twenty somethings.
