Very simply, you think that the more atmosphere there is above you, the more things weigh.
Yes, the more pressure that is upon any mass withing in.
This is dependent on how high the dome is above you.
Nope. Not al all and this is where I lost you but I think I get your thoughts.
You see, it look like you are implying that we live under the higest pressure. We don't. The highest pressure is what you know as the north pole. It's what's feeding the life giving energy (sun) but we won't go into that unless you want to.
The least pressure on us would be the furthest we could go to the ice dome foundation which would be elevated anyway, as the Earth isn't flat as a pancake, it's slightly concave, but nevertheless, let's move on.
Where we live is the equator part and a little further towards the centre, not close to the centre, I mean many thousands of miles away from it.
This explanation sort of works with mountains but it turns out that g doesn't seem to be exclusively dependent on elevation.
It dependent on the energy needed to elevate a mass/density.
So when looking at the values of g around the world it is clear that if there is some physical barrier there, it is not making any sense as it pertains to your description of the dome because g is least at the equator and most at the poles.
As I said above.
So denpressure was already resting in peace but even if we pretend that you have debate skills and pretend that by some miracle you've convinced us that it is real, it doesn't imply that there is a dome as you've described and it also doesn't even imply that the earth is flat. Actually considering the data, it looks more like a round object than anything else.
Denp4ressure is never resting in peace, it's always there however minute.