Hey OP,
Rinses/Semi-permanent helps gives my fine hair that thickness that you speak of. When I was relaxed (I'm currently natural) I used Clairol Natural Instincts for "heavy" hair....Actually I think it is considered demi-permanent hair color now that I think about it.
Anyway, it also left my hair shiny without it being weighed down.
I have attached an old photo for comparison. These are obviously on different dates as my hair is longer in the second photo. But, if you look, you can see that my hair is noticeably shinier and thicker in the second picture. It is definitely due to the Natural Instincts.
The first photo shows my natural hair color.