The person giving those measurements apparently had the ability to measure their ingredients by volume and then weigh each ingredient.
Beeswax comes in all kinds of shapes and forms, and I imagine candelilla wax does too. That's why there is such a difference in the volume to weight ratio for each of the two solid waxes. For example, 1/4 cup of a solid wax is not going to weigh the same as 1/4 cup of the same wax if shaved on a food grater. I honestly doubt other people will get the same results if using volume measurements, unless they get the same exact products the author used.
In addition to that, candellila wax is much firmer at room temp than beeswax, so the "vegan" version of this recipe looks like it's been adjusted to use more oils and less wax.
"...Its the bits that say "for the vegan recipe use 156ml" - I probably could do the math..."
The approximate conversion for many fats is 0.92. Use this to change mL to grams or to change fluid ounces to weight ounces --
Weight = 0.92 X (Volume) = 156 mL X 0.92 =143 g
I'll also mention that even if you follow the recipe to a "T", you will probably have to adjust the proportions of the ingredients to suit your needs. A lot of people show up on SMF every fall/winter wondering why their lotion bar or lip balm is too hard or too soft and how to fix it -- use this recipe as a general guide; it's not a surefire recipe that's going to be perfectly suitable for everyone.
So don't obsess too much over getting the numbers exactly right for this recipe, because you're likely to change them anyway. Just sayin'.....