Strongly recommend the concept of using two pieces of thinner lumber with glue and screws to make our larger pieces. There is a reason glulam beams are significantly stronger and lighter than traditional lumber. You can look up the properties of all these wood profiles to determine your deflection too btw. Google beamboy for a free program to calculate the deflection after you look up the moment of inertia (moi) to plug into the program. And deflection is but one piece of the puzzle; buckling and racking are the other much more dangerous ones to worry about. Again, follow rocketengineers advice on pockethole screw attachment for all of this too so this doesn’t collapse on itself.