Need Help with Accessory Weights

Hi. You should always start by cloning something vaguely similar and studying it.
The hair strand is in the hat area, so clone a hat. You will see that the hat is assigned to the head bone only. Yours is assigned to the breast bone as well. In your case, simply deleting the breast bone is enough. So select b__CAS_R_Breast__ and click on the - button (step 2, ignore everything else)

Next, normally cas items morphs when you adjust the shape of the body. However, does this hair strand needs to morphs? Technically no, so you can vertex paint it with black ( do only 2, 3 5)

Next, you'll see that the hat has 2 uv maps. uv_0 is responsible for projecting textures while uv_1 is for morphing. You should rename UVMap to uv_0. Since your mesh does not need to morph, you do not need to create uv_1.
Now, when you put the hat on the sim, the hair shape changes . You do not want this to happen when you put this hair strand on a sim. You could edit Region type but it would be easier to just clone earrings.
And for that reason you could also put the hair strand uv island in the space meant for earrings so that all this space in the hat area is not wasted.