Hostas. Or just mulch.

Westy

Corsican mint. It might take a while to fill in densely enough that it well keep the weeds at bay. But it loves shade.

Pachysandra can take that much shade, can't it? If it's okay for your zone.

My suggestion is more of an architectural landscape design one...., if that were my yard, I would pull out all the weeds, level it out, put down some weed barrier cloth and cover with nice rocks. You could additionally do a nice lattice with trim to surround from the top of the deck to the ground, and plant some pretty flowering vines on the outside such as morning glories, butterfly vine, etc. If you made one end accessible with a lattice gate, you could use it for winter storage for excess patio furniture, etc.

Good luck!

That's a great idea hollandgirl! I'll have to look into that. I guess I can do to Home Depot or Lowes for lattice?

I had the same issue with my deck. I planted vinca minor during the spring and it is taking over nicely. It can be a bit invasive so you would need to cut it back periodically. Good luck!

My deck has the lattice solution - I wouldn't do it any other way!! The vines love it, and my dogs use the shade during the heat of summer. HD and Lowes both carry wooden lattice. Good Luck - You'll LOVE it!!