Why does gravity cause acceleration?

[Fly135]

If gravity is just the effect of warping space, then why does it cause acceleration?  For example, an object is dropped from a height and moves towards the ground.  When the object reaches height/2 another object is released from that location.  Since they both exist in close proximity relative to the earth, shouldn't they both be in the same warped space?  Hence, they should be moving at the same speed because the warping of the space for each object would be the same.

I could see that the closer to the earth, the more the warping of space and consequently some "apparent" acceleration would occur.  But an object released should immediately move at the speed of the warped space.  IOW, the apparent acceleration would be infinite because the object isn't actually accelerating but simply sitting still in space that is moving relative to the massive object.

Of course this isn't what actually happens.  But it would help to better understand the actual mechanism behind gravity if I knew why it doesn't work like in my question.

[Ghideon]

13 minutes ago, Fly135 said:

If gravity is just the effect of warping space, then why does it cause acceleration?  For example, an object is dropped from a height and moves towards the ground. 

Isn't it the other way around? Objects that are dropped from a height moves towards the ground in free fall. Objects prevented from falling are accelerating. Some thought experiments as a starting point for discussion:
If you stand on a scale on the earth it shows your weight.
If you stand on a scale in an accelerating spaceship, far from any source of gravity, the scale will show your weight if the acceleration of the spaceship is (approx) 9,8m/s²
If you try using a scale while falling towards the ground the scale shows zero.
If you try using a scale in a spaceship far from any source of gravity the scale shows zero.

[Markus Hanke]

2 hours ago, Fly135 said:

If gravity is just the effect of warping space, then why does it cause acceleration?

It doesn’t. When you put an accelerometer into free fall, it will read read exactly zero everywhere and at all times. There is no proper acceleration in free fall, and thus gravity isn’t a force in the Newtonian sense.

[Tutoroot]

Acceleration is a change in velocity, and velocity, in turn, is a measure of the speed and direction of motion. Gravity causes an object to fall toward the ground at a faster and faster velocity the longer the object falls.Acceleration is a change in velocity, and velocity, in turn, is a measure of the speed and direction of motion. Gravity causes an object to fall toward the ground at a faster and faster velocity the longer the object falls.