Botanist would support Carpenter and Weaver. (Actually, Weaver alternates. In some tiers its primary resources come from botanist and through other tiers they come from combat drops.)

Miner would support your Goldsmith.

Alchemist is a bit hard to tell. It doesn't really have a primary resource exactly, but more an assortment of miscellaneous items, some coming from each of the gathering classes and some as combat drops. (Most of the other crafting classes need an assortment of miscellaneous items in addition to their primary resource type.)

And yes, Weaver and Leatherworker go well together due to their intermediate resources. Weavers use some leather in quite a few of their recipes and Leatherworkers use cloth in some of theirs. (The basic pattern in most crafting is that raw resources collected by gathering classes or combat drops are first crafted into intermediate resources and then those are made into finished items. So a Leatherworker will use hides to make leather, then use that leather to make equipment. A carpenter will use logs to make lumber, then use lumber to make their items, etc. But some of those intermediate resources cross over, like a Weaver needing both cloth and leather to make many of their items.)