Just going to point out that you can have weeds
and have a 5-star island, as I had quite a few and still managed to grow lily-of-the-valleys. You just can't have so many that it reduces the rating (most likely tied with the scenery portion of the rating system). Not sure how many that would be as I believe it depends entirely on how many scenery points that you have.
Here's a
link to the full rating guide from the companion guide someone posted awhile ago. Mentions nothing of weeds, but I assume they still detract points from the scenery section. The weeds also may count as "clutter" (unsure of this), so if you have more than 45 weeds in an 8x8 block, Isabelle may complain. Mine were spread out myself, which may be why I still kept my 5-star rating.