Eles entregaram a ele no primeiro livro, após o incidente com as letras ... mas, quanto a mantê-lo, não me lembro de ter sido expressamente declarado, mas acredito que era devido a eles terem medo do que ele poderia fazer com sua magia, uma vez que ele aprendeu que tinha e como usá-lo.
Do mesmo livro:
Underage wizards weren’t allowed to use magic outside of school. Harry hadn’t told the Dursleys this; he knew it was only their terror that he might turn them all into dung beetles that stopped them from locking him in the cupboard under the stairs with his wand and broomstick.
(Enfase adicionada)
Desde que foi onde ele ficou antes, parece bastante consistente com esse ser o motivo.
No primeiro livro, perto do fim, vemos:
“Hope you have—er—a good holiday,” said Hermione, looking uncertainly after Uncle Vernon, shocked that anyone could be so unpleasant.
“Oh, I will,” said Harry, and they were surprised at the grin that was spreading over his face. “They don’t know we’re not allowed to use magic at home. I’m going to have a lot of fun with Dudley this summer…”
Além disso, acho que eles tinham um pouco de medo do que o Mundo Mágico pudesse fazer em resposta ao abuso de seu 'Herói'. Isso não resultou em um bom tratamento, mas pelo menos os exagerados 'o mantêm sob o controle. a questão das escadas foi embora. No geral, uma versão menor da proteção que ele recebe no final do Prisioneiro.
“It’s not,” said Harry cheerfully. “It’s a letter from my godfather.”
“Godfather?” sputtered Uncle Vernon. “You haven’t got a godfather!”
“Yes, I have,” said Harry brightly. “He was my mum and dad’s best friend. He’s a convicted murderer, but he’s broken out of wizard prison and he’s on the run. He likes to keep in touch with me, though… keep up with my news… check if I’m happy…”
And, grinning broadly at the look of horror on Uncle Vernon’s face, Harry set off toward the station exit, Hedwig rattling along in front of him, for what looked like a much better summer than the last.