We can assume that the addressed audience of this sentence is an adult woman. From one perspective, the adult woman and the little girl are the same person. From another, they are not. The little girl no longer exists and is not the same as the adult she later became. I have no reason to suspect, for instance, that this woman over-waters her plants.
The model sentence assumes this second perspective.
The woman is represented by a second-person pronoun: "you". The phrase "a little girl" is a third-person noun phrase. The antecedent of "she" is "a little girl", making the third-person pronoun form appropriate.
The little girl isn't even real. She's a product of the speaker's imagination or memory, nothing more than some hypothetical figment. She might never have existed at all, outside of the speaker's perceptions. We can treat her as an eternal concept.
As an eternal concept, that it agrees with a verb the present tense makes sense. In the speaker's memory, the little girl still doesn't know when to stop.
Your proposed revision takes the other perspective. The woman and the little girl are the same person, but at different stages of her life. The "you" of "you didn't know when to stop giving" has the same antecedent as the "you" earlier in the sentence. Both refer to the addressed adult woman.
Your revision uses the past tense. This is sensible because that stage of development is in the adult woman's past.
The "you" and the "she" exist in different timeframes. These different timeframes lead to different implications.
Your revision implies that the woman now knows when to stop. She didn't know as a child, but the past tense lets us safely assume that she has stopped not knowing. The difference between the woman and the child is established.
A different revision uses the present tense throughout:
I still remember you as a little girl who over-waters plants because you don't know when to stop giving.
This implies that nothing has changed. The woman didn't know when to stop as a child, and she doesn't know when to stop as an adult. The similarity between the woman and the child is established.
In the original, the third-person "she" is conceptually distinct from the second person "you". The little girl eternally lacks that knowledge. From that sentence, we have no idea at all whether the adult woman knows. The original sentence gives me no reason to assume that the adult woman over-waters her plants, but it also gives me no reason to assume that the present-day woman doesn't over-water her plants. The difference or similarity between woman and child is left unspecified.
That lack of specificity is not possible with the pronoun "you", but it is possible with the pronoun "she".
That's the difference that a shift in perspective can produce.