I might add that this balcony is not covered, only the soffit.

It's not covered and it faces west? It's going to be hot as blazes in summer unless you live in a far northern climate. Hopefully it's a wide soffit?

As for how to build it, I'm sorry but I will defer to the builders and architects on this forum.

Not enough info. What kind of balcony? Similar to which pic?

Those "hole in the roof" balconies are very hard to get right. The slant has to be correct, and if the house settles wrong, they will trap water and rot.

Can you change it to the open kind, or a 2nd story veranda? They are more forgiving because there are fewer places to trap water.

Well, exterior balconies over interior occupied space below may be the most challenging of all balconies. It all depends on the design. And the workmanship. The challenge is to keep water out of the house at the upper and lower levels, while also maintaining the materials exposed to the weather. Easier said than done.

We have a balcony off our master suite that sits above the covered porch below and here's how our builder handled it. The balcony is also covered and both the balcony and deck extend 8 feet out from the house. The deck below is cement with a blue stone tile, but the balcony is wood structure with Azek decking. The balcony joists run perpendicular to the house and are shimmed to slope away from the house. The plywood decking that covers the joists are further waterproofed with a single contiguous piece of rubber that also runs up the side of the house. Sleepers are installed on top of this so the Azek has something to attach to. The wood support posts are flashed at the base to help prevent water intrusion. When planning the balcony, you have to account for the thickness of all this stuff.

Alternatively, there are some commercial products available that install in the joists of the above deck to capture and route water.

The detail depends on what is below.

That is going to need to be disassembled and redone.

That sidewall interface? No, I'm not wrong. You're not looking at the big picture.

I hope so.

best of luck.