Thanks - that looks right. I had cut open a fruit and thought it looked fig-like, but the leaves looked nothing like a true fig tree. It looked for all the world like a tree. I guess it must have climbed a tree and taken over.

It looks like a weeping cherry. The branches are meant to hang down low. If you cut them back you will ruin the shape of your tree. Google image 'weeping cherry' and see how good a well-grown specimen looks.

That's what I thought from the compound leaves, although I've never seen Fraxinus leaves that slender. But the bark doesn't look like Fraxinus to me; and it doesn't look as obviously opposite as Fraxinus does. I'll have to go back in the fall and see what the fruit looks like--

Some vines can weigh down or girdle trees and branches, or sprawl along the ground and crowd out all other vegetation. Take it case by case. If it damaging a tree you like on your property, get rid of it. If it is invasive and sprouting everywhere you dont want it, get rid of it. If its just climbing and both seem okay, then leave it unless research has found it to be an invasive species in your area. The vines close the edge of the forest and shade the interior.