I base most of mine off of the sweetness of Kool-Aid: 2 cups (white sugar) per gallon which works out to be close enough to 1 lb per gallon to be an easy rule of thumb.
Honey is significantly sweeter than white sugar, so use less of it. How much less is up to you. Maybe make some smaller test batches without carbonation to see if the sweetness is about right. If you start out with not enough, you can always add in more, but you can't really go the other direction without diluting root beer flavor.
Brown sugar has the same sweetness as white, but unless it's very densely packed, it's not the same cup for cup as white on a weight basis. You end up with less weight in a cup of brown sugar than in a cup of white sugar.
If you look at commercial root beer sugar content, it's a little bit higher than other sodas, if that helps you at all.