And this 'equalizing around and under' is at the same time accelerating it up, and pushing it down?
Try not to ignore the nergy applied to the ball, as in you throwing it up. The energy you apply and the density of the ball, determines how much air you compress. That compression of air has to be pushed around the ball. Because you threw the ball up, you created a lower pressure under that ball due to compressing the air above that ball. That air then cannot stack on that ball due to the open space you threw it in, so it is pushed around the ball, or to make it simple. It springs back into shape at speed around the ball to equalise the lower pressure under that ball you created by throwing it. Once that energy is resisted by that compression, that last compression forces that ball back down against the last low pressure created and now the opposite effect happens, where the density of the ball, now compresses the air under it forcing that air to equalise the lower pressure created, all teh way back to where the ball came from, which is where everything comes from. The ground or any place that can create a resistance immediate to that balls density, which could be your hand catching it or falling on a shed roof, etc.
If the equalization effect is sufficient to keep the ball going up, even against the greater pressure on top, why does a barely measurable difference push the ball towards the ground at similar force when the ball is at rest?
As above.
Shouldn't the ball just float around in the first place?
How can it float around? It's always under pressure.
How does the weight of the ball come in to this, if it's an air-filled balloon or a bowling ball of identical size and shape, why do they fall at a different rate, surely they are displacing exactly the same amount of air and so generating exactly the same pressure differentials?
The more dense an object is, the more air it can displace and faster, which is why a bowling ball can fall faster than a beach ball that is merely just air and a small amount of plastic.
You'll never grasp it because your mind immediately goes into gravity mode. You simply can't let go of it, even though gravity makes no sense and is pathetic and cannot be explained as a force. It just is and that's that.
If you can't grasp it, then no problem.