If you reject that force, you end up with this:
Where there is no pressure gradient.
This is a better set up. If you just use F without any minus then this is the deal.
No need for any W or G. It's just nonsense.
Again, you are the one spouting nonsense.
If you just use F, there is no gradient.
The pressure is constant throughout.
You need that extra force, which you dismiss as nonsense to create the pressure gradient.
The bottom layer is under immense pressure from all the above layers that are stacked upon it.
The next layer above that is also under immense pressure but not quite the same as the below.
Why?
That is the big issue you can NEVER explain.
The only thing in your model pushing that bottom layer down is the air above.
The only thing in your model pushing the above layer down is the air above.
There is no extra force to make that intermediate layer push down more.
Again, you can try this by turning the system sideways, and using ANYTHING as an analogy.
If you push a bunch of springs or sponges or whatever against a wall, the pressure is the same throughout.
With the wall on the right:
The right layer is under the "immense pressure" from the left layers pushing it into the wall.
The next left layer is also under "immense pressure", and that is the same pressure as that on the right most layer.
It doesn't matter how many layers you have, or how much force you use, there is no magical gradient.
It can also be clear to go from the other way.
The left most layer is just being pushed by you or whatever. This uses the layer to the right as resistance, by pushing on it.
This transfer the push you are applying to that layer, effectively pushing it with the SAME force, not a magical increase like you want to pretend.
The layer
This continues all the way to the wall.
The push and resistance are balanced, and there is no increase in force/pressure at all.
Now, as a different analogy, one which actually uses the W you dismiss as nonsense:
You have a bunch of people pushing right into the wall.
They are now using the ground as resistance to push to the right.
Now the person furthest to the left has no one pushing them, but they push against the ground into the next person along.
This next person along is being pushed by the person behind, and is also pushing off the ground. This allows them to push with even greater force into the next person.
You could consider them as pushing on the people to the left using the people to the right AND THE GROUND as resistance.
Now this continues, with the force building until the person next to the wall gets crushed from the force.
As each person is using the ground to apply an additional force, the pressure builds.
Again, no extra force, no pressure gradient.
So this extra force is what you need to explain, or you need to explain how the air magically pushes down with a force greater than the force pushing the air down.
I'm absolutely sure you'll reject it and also claim I don't explain anything.
Perhaps when you stop with the pathetic dismissal and actual deal with the issue I will stop pointing out that you are continually deflecting from the issue.
This isn't directly for you, it's just conveying the message through you. It's for those who actually want to try and understand.
Again, the fact I repeatedly explain why you are wrong, and you continually deflect from that shows I do understand.
What it seems to be is for those you hope will just blindly accept whatever garbage is put forwards to pretend the globe is wrong.