When mixing new concrete, is there something I can mix in to stop moisture from weeping through?

Weeping through what?

weeping through what?

Through a 4inch conrete slab

Do you mean ,from coming up through the floor it self

Yes

Put 3 mill plastic down over top of the dirt and pour the concrete right on top of the plastic, this will keep the dampness from coming through.The only thing with this is ,the concrete takes longer to set up. But it will remedy your problem.