Re: Wood deck over concrete patio?
Regardless of what you do, you'll have to kill that mulberry or else its roots will continue to destroy anything you put there. Mulberries are very invasive and destructive.
As to what to do with your space, it really depends on your needs and desires. Concrete will be the easiest and most durable, as long as the mulberry is not allowed to get near it. A deck tends to be a little more elegant, but requires upkeep to stay looking nice and rot free.
Good airflow under and around a deck is a must, though even with this, unless it gets a healthy dose of sun every day, it's going to be more prone to rot issues, even with pressure treated materials.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!