Vibration and frequencies create pressures and energy.
You feel the heat on your back because of the vibration/agitation of molecules.
What are they doing?
They're expanding and contracting causing that vibration/agitation.
And that is where your idea completely breaks down.
You doubt gravity, fair enough. It is an odd concept. It is said to be a force that is created by all things, it surrounds us, it penetrates us, it binds the universe together. Basically if something has mass (standard definition of mass) then it has a gravitational field and that is an attractive source towards it. The bigger the mass the bigger the attractive force. The earth is rather large so we are significantly affected by it's gravitational field, we can feel it where as we can not feel the weak gravitational field from something much smaller, say a near by cheese sandwich. Where else is there an invisible force that can attract objects together? I can see why it seems far fetched and it comes down to looking at the evidence for it or against, vs alternate theories. But it is the simplest theory that fits all observational evidence even if we don't fully understand how it is created or actually works.
So you have gone down the skeptic route and replaced with an alternate theory, fair enough. You don't want to believe in an invisible force that just makes objects fall to the ground. But when we break it down, you have replaced it with an invisible force that just makes objects fall to the ground, only with a lot of complexity.
Lets break this down. Atmospheric stacks make objects fall. It is established that pressure is higher and the air is more dense (standard definition of density) at sea level and less dense with lower pressure on a mountain top. It then stands to reason that as you go up there is a linear decrease in pressure and density. It is how an altimeter works, so this is proven pretty reliably and we can hopefully agree.
Air is a gas, or more accurately a mixture of many gasses, so lets concentrate on one of the main components that we need to survive, oxygen (we could equally pick another). Your claim is that an object placed in a lower pressure stack layer is under more pressure at the bottom than at the top. This is correct. If it works on the scale of a mountain then it works on the scale of a rubber ball, only a ball is so small, the effect is minute and almost unmeasurable, but it is still there. That means there is more pushing on that ball at the bottom than the top. This effect of greater pressure at the bottom causes the object to fall. That makes no logical sense and it is the wrong way round. An object will move to where there is less pressure acting on it. This can easily be simulated. You can create higher pressure by blowing. Try blowing on one side of something and see which way it moves, away from or towards you?
But it then leads to the question I asked, how do these stacks form? In the conventional world, gravity. Gravity acts pulling the molecules of the air down, but can only pull them together to a certain density at which point there is just not enough space. It is hard to word that but what I'm saying is gravity is not strong enough to pull all the oxygen molecules together to form a crispy solid oxygen crust. Add to that wind and all other forms of air currents like thermals, or atmosphere is constantly being mixed up. It makes the air more dense at ground level but not compressed into a liquid or solid.
You claim the molecules are crushed smaller and smaller into a higher density and this causes them to compress. No. A gas is made of many molecules with a lot of space between them. When they are forced (pressure or lowering temperature) together, that forms a liquid. Force it more and it becomes a solid. If you compress a gas, say in a large piston, you compress the space between the molecules not the molecules themselves. Many reputable sources say that molecules or atoms can not be compressed. I don't have a powerful enough microscope to argue either way, but I suspect neither do you. If you could compress a gas enough so there was no space between and the molecules started pressing into each other, you could have created a solid under immensely high pressure. That is not what we have to breath on the surface of the earth. Boyles law also says this would create a massive temperature increase, this doesn't happen.
What your theory is that the molecules shrink because of the pressure, to create a higher density, but that higher density is created by pressure and that pressure is caused by the stacked layers forcing stuff down. I.e. it creates itself. Realising this causes a problem, you have added an invisible force pushing everything down. You now have individual molecules being crushed so much smaller by this invisible force, but we don't get crushed. The force is enough to crush molecules but not force them so close together they form a liquid or a solid. Not really likely is it, when you think deeper on the subject?
But there is this force or energy coming from somewhere and it is the centre of the earth, reflected off the dome and falls as sunlight. So the modified claim is that sunlight forces objects downwards, even at night (standard definition of night). This light falls from above and when it reaches ground level it crushes molecules more than it does higher up. How, why? It has just travelled thorough kilometers of air, why does it affect the stuff furthest away more than the closer stuff? Even if it was this, it makes no logical sense that it would just crush gases together, crushing more the further it travelled.
At the end of the day, you need a force that makes the air denser at the bottom and that force is gravity.
And of course, there is no evidence molecules can be compressed, there is no evidence there is falling magic sky vibration energy joining everything together, there is no evidence that atmospheric stacks force objects down (clear evidence they do not) and no evidence of this energy coming from the central earth. This whole model is completely without any evidence for any of it, other than perhaps a claim that you can personally feel it.
What you have done is doubted "magical invisible" force with a simplistic model, dismissed all evidence for it and replaced it with a "magic invisible" force with an incredibly complex model with no evidence for it. This is a trait common to conspiracy theorists. Take something simple like sunrise and sunset. Spinning ball, sun relatively remains in the same place, sun appears to rise and set to observer on ball. Easy to simulate with a physical model or a computer. There are many conspiracy theorist models, all incredibly complex and none that actually work. There was one which talked about the sun sliding backwards and forwards on an invisible table FFS.
I'm afraid this one has to go down as a complete fail. It just doesn't work, no matter how free you think your mind is.