When you refer to horseweed, what plant are you referring to? What I usually think of here as horsweed, is in fact giant ragweed, gets about 5 to 7 feet tall with thick stalk. As kids, we pulled it up in fall, the root is long and pointed, and used them as spears. I am assuming your "horseweed" may be a smaller plant.
And the Ailanthus you refer to....that is what is commonly called Tree of Heaven....is that correct?
Thanks,
Harold