If air (or fluids in general but especially air) didn't move, would it still exert pressure? If gas particles in air were stationary. As usual, they had very weak intermolecular spaces and forces but they didn't move, would they still exert pressure on objects around them?
 A: When air is still, air molecules are bouncing around. The pressure they exert is from all the recoils. You are likely thinking that without recoils, there would be no pressure. But that isn't quite right.
You also have to consider the reason they keep coming back and recoiling again and again. When they fly away, they quickly bounce into a molecule and get bounced back toward you.
The reason that all these molecule hang around the surface of the earth is gravity. All the molecules above them push down on them. The total force they exert on you is the weight of all the molecules above you.
If they slowed down enough, they would condense into a liquid or freeze into a solid. The weight would be the same.

Let's take this in pieces. I will skip over the math and trust the results are plausible to you.
Suppose you have a ball of mass $m$ sitting on top of you. $F = mg$
Suppose the ball bounces up and down. Suppose it spends $1/100^{th}$ of the time in contact with you being pushed upward with constant force. The rest of the time it is in free fall. You can show that the force you exert is $F = 100mg$ during that time, and $0$ during free fall. Since every force has an equal and opposite reaction, the ball exerts $F = 100mg$ downward on you when it is in contact.
Suppose you have $100$ balls sitting on you. $F = 100mg$ all the time.
Suppose you have $100$ balls bouncing on you out of phase, so that $1$ ball is always in contact. Again, $F = 100 mg$ all the time.

Now suppose we have $2$ layers of balls. Each ball that sits or bounces on you has a ball above it sitting on it.
If the top balls sit on the bottom balls, it is just like having balls of mass $2m$. It doesn't matter if the ball pairs are bouncing or sitting, $F = 200mg$.
Suppose the top layer is bouncing. We will arrange things so that each time the bottom ball reaches its peak, the top ball bounces off it. As before, it doesn't change the average downward force on the bottom layer of balls. The top layer exerts $F = 100mg$ on the bottom layer. This throws the bottom layer balls at you harder, so the bottom layer exerts $F = 200mg$ on you when they bounce.
