Acostumbraste comes from the verb acostumbrar, meaning 'to accustom' or 'to get used to'. In this context, it's used in the preterite tense, 'tú me acostumbraste', meaning 'you accustomed me' or 'you got me used to'.
In the song, the singer says, "Tú me acostumbraste a ser como un niño" (You accustomed me to be like a child). This line beautifully conveys how his lover has made him feel safe and cherished, like a child, highlighting the deep emotional bond and dependence he feels.
Leo Dan sings a love song built on extravagant promises. If his partner asks for the moon, he'll bring it down for her; if she asks for a star, he'll go up there and get it. It's over the top on purpose, a way of saying there's nothing he wouldn't do for her.
Underneath the promises is a plea. He asks her never to say she doesn't love him anymore, because those words hurt him deeply. He'd rather give his whole life and prove his love than hear that from her.
The song circles back to the same chorus again and again, like a vow repeated for emphasis: ask me for anything, just don't take your love away.