How is the あげたい working here?

Question

On a TV show, an idol was given this task to think of:

心が晴れやかになる一言
'A word (or phrase) to lift someone's mood'　　(My loose translation)

The idol responded:

アナタの心の雨を[止]{や}ませてあげたいな
'Let me try and get rid of that cloud hanging over you'.　　(Very loose translation, I know)

So, more literally translated, I guess it would be:

'Let me stop the rain in your heart'.

I would like to know how あげたい works here. Is it working like:

I'd like to give you my action of stopping the rain in your heart

Or is it working differently?

Answer 1

〜てあげる is the form of "doing X for someone". The quote is just the combination of that and the 〜たい form (want to do). So it is "I want to do X for you". Of course, remember that 〜てあげる should not be used for 目上の人, and even when used properly might sound patronizing in the wrong context.