Yes, those are weeds and the tree is especially a weed! That is "princesstree", Paulownia tomentosa, and it is a category ONE invasive plant in Georgia.

Holy cats! I'll be sure to rip that weed tree out of the compost heap and toss it straight into the trash bin as soon as I get home. Thanks so much!

Now, how do I keep those wretched weeds from returning? Should I go ahead and cover with newspaper & pinestraw and plant my tree?

Now, how do I keep those wretched weeds from returning?

Number one is: don't let them go to seed. Rip them out right away.

Number two: prevent any seeds from germinating. That can be done using a pre-emergent (preen is one) or using corn gluten (a non chemical approach). It would be helpful to figure out the name of the weed to determine when it germinates. It is tedious, but you could flip through the link below to try and find it. Or just assume that it germinates in the spring and follow instructions for spring germinating weeds.

Scratching up the area now with a hoe might get a bunch more to germinate and then you can kill them. Newly germinating seeds are easy to pick out or destroy by gently raking them out. In general, soil disturbance causes seeds to germinate because you expose them to light.

Perhaps someone else could chime in on the layer of plastic approach.

Here is a link that might be useful: Virginia Tech weed site

Thank you very much! I yanked them out and covered the area with grass clippings and newspaper.