I wax my lip- not because it was dark but I just hate hair. The color and thickness feels the same, but it almost seems like there's more hair. I've read that waxing messes up your natural hair cycle for growing and losing hair, and will put it all together which is why women seem to think they're growing more when really they're growing all at the same time. You'll probably have to do it every 2 weeks which can be expensive so if you're brave I'd suggest trying at home.
I've never had my lip waxed but I do get my legs waxed.
Waxing grows back MUCH slower than shaving. Shaving cuts the hair right at the skin, so if the hair grows the tiniest bit, it is noticeable. Waxing pulls the hair from its source, so the hair is actually completely gone right afterward. So, because it is gone from even the follicle, it seems to grow back slower. After lots and lots of waxing though, sometimes the follicles themselves are ripped out, which results in less hair permanently.
It will grow back thinner than shaving too. Shaving creates a rough point, which is stubble. For waxing, when the hair grows back, it is a completely knew hair with a soft, fine tip.
You need to wait about 3 weeks, sometimes more, between waxing so that enough hair can grow enough for the wax to grip.