Electric field has nothing to do with density of the object.  If you are saying that the force on the object is due to the electric field, we can stop right there.  Electric field would have no effect on the brick made out of plastic, and yet the object does have weight and is exerting force on the ground.

Your argument that the density of the object is influencing air pressure to act on the object is just not true.  Air pressure is the same around a heavy object and a lighter one.  Same pressure is all around us.  It is measurable.

What is responsible for the force the object exerts on the ground? Air pressure or the electric field between the dome and the ground?

BTW, if the electric field is responsible for all the forces heavy objects exert on the ground, you would have to have extreme electric field strength and that field would have to be stronger around heavy objects and go to almost to zero around an ant walking on the ground.  Actually, ants would not be able to walk, as everything else would be under extreme forces of attraction.

Do you even understand what you are proposing?  All objects would have to be positively charged to be under any force due to the electric field you describe. At the ground level they would be very heavy according to Coulomb's law.  You would be simply ripped apart. Never mind that all the electronics and the computer on which you write your nonsense would simply not work.  

If only air is positively charged, then air molecules would be attracted to the ground and you would not see a penny dropped in a glass of water drop to the bottom of it.  Again walking around on such a planet would be impossible, never mind breathing or pumping blood to your organs.

PS. I'm just being entertained.  I feel like I am talking to a small child, but I'm being sincere to point out the fallacies in you logic to lead you out of your madness.  I tried to do the same thing with CoinCube and BADecker with a limited success.