In the movie Star Wars: Episode I Anakin Skywalker is a child and Padmé is a young lady. Their relationship is that of a child and a lady.
But in Episode II Anakin has aged into a young guy even though Padmé appear to be almost the same age and they are having a lover's relationship.
What is the logic behind this? Doesn't Padmé age? Is there any in-universe explanation?
In 'The Phantom Menace' (set in 32 BBY) Anakin is aged 9 and Padmé is 14. He turns ten during the film.
By the time of their (sexual) relationship in Attack of the Clones, (set ten years later, set in 22 BBY) he was 19 and she was 24.
The name resonated in young Anakin’s heart and soul. He hadn’t seen her in a decade, not since he, along with Obi-Wan and Qui-Gon, had helped her in her struggle against the Trade Federation on Naboo. He had only been ten years old at that time, but from the moment he had first laid eyes on Padmé, young Anakin had known that she was the woman he would marry.
Never mind that Padmé was several years older than he was. Never mind that he was just a boy when he had known her, when she had known him. Never mind that Jedi were not allowed to marry. - Attack of the Clones: Official Novelisation
As to why she doesn't appear to age (much), I think we can put that down to an excellent moisturisation regime.
Padmé ages from 14 years old in Phantom Menace to 24 years old in Attack of the Clones.
Assuming the humans of Naboo follow the same growth as Earth humans, the females usually reach adult height between ages 14-16, according to the CDC: http://www.cdc.gov/growthcharts/data/set1clinical/cj41c022.pdf
From this, we can assume not much physical changes happened in Padmé's body during these 10 years.
Also it is widely known that Naboo's royal makeup artists are very good. All of the handmaidens are trained in makeup techniques.
So, for a young queen, the makeup could be made to make her look more mature.
And agreeing with Richard, since it is a planet with extensive water features, the moisturization.
Actually Anakin was 9 but turned 10 by the end of the film The Phantom Menace and Padme was 14. So if Attack of the Clones is 10 years later that would put Anakin at 20 years old and his birthday would've had to be days before they were assigned to protect Padme from the assassination attempts. So therefore she is 24 or 25 in Attack of the Clones at the time and Revenge of the Sith is 3 years later, putting Anakin at 23 years and Padme at 27 or 28.
Padme was queen at a very young age the make up made her look mature and older. In The Phantom Menace she was 14 and Anakin was 9. In Attack of the Clones he is 19 and she is 24. In the last two episodes they don't look like they are years apart. Natalie was 16 and Jake was 8.
