The force to close the door is desired. It helps your A/C work better.
Atmosphere is at the pressure of 14.7 PSI because of the weight of the air above you. Wind and storm activity changes that pressure ever so slightly, let's say a 0.1 PSI difference, heck, let's say 0.01 PSI, that being very tiny compared to 14.7 (1/1470th in fact). What does that do to a door? Well a door is, say 40"x80", that's 3200 square inches, so
3200 sq.in. x 0.01 lb /sq.in. = 32 pounds. (about 15kg).
So that tiny little bit of pressure differential makes a big difference in door-close effort.
And it goes to show you just how much a little bit of wind will make a difference in "helping" you to close that door. Most likely with your windows open, you've been catching a little bit of wind, and that's been "helping" you close the door, hence, the sense of weightlessness. You've been experiencing that magic and you want the magic back.
Now you have the exact opposite: you have that room sealed up like King Tut's tomb, so you aren't wasting air conditioning, which is exactly what you should do. Now when you're closing the door, you're creating a pressure differential. Consider the last 2 inches of door closure when the door is starting to plug the opening. That's an average of 1" of movement across the entire door, x 3200 square inches of door, so 3200 cubic inches or about 2 cubic feet. Assuming 10' ceiling your room is 500 cubic feet. So as you finish closing the door, you're effectively increasing the room size by 0.4% and lowering air pressure in the room by the same. That times 14.7 psi = 0.06 PSI, 6 times stronger than what's described earlier or 192 lbs. closing force. It's not that bad because your seals aren't perfect.
Of course if you just close the door slower, air will have more time to equalize as you close it.
So that force to close the door is a good thing.
If you wanted to eliminate that, you'd need a large enough opening to allow 2 sq.ft. into the room in the fraction of a second it takes to finish closing the door. That would be window-sized obviously. If you want to run your A/C with the window open, hey, it's your electric bill.
Now if you want to keep the cool air in, you could possibly use a heat exchanger, which they do make. But it would have to be quite large or several of them to allow that much flow in that fraction of a second.
You could also put a spring or counterweight on the door, but that means "easier to close" also means "harder to open".
You could also put a motor-drive on the door so you can just push a button; these are made for commercial doors where people in wheelchairs need to come in and out.