Because as you get closer to a mass the grid is distorted more - the more the grid is distorted the further you go in a slice if time. Going further in a slice of time is fundamentally what acceleration is.
As you get further away from a mass the grid is distorted less therefore you travel a shorter distance in a slice of time.
This is easier in 2D where the Grid can be considered this way. With no mass we have a square and therefore no direction (m is equal to r) Add two masses that influence each other. Now think of the grid as an isosceles trapezoid with the heavier mass below and the lighter mass above, the height is r and m is effectively our direction. You can consider the direction of movement as being represented by the line at the base of the trapezoid. So some matter directly between the centres of mass of two stationary objects will move towards the larger mass.
This is also why you feel gravity when you accelerate - You are ‘pushing’ past the particles, the faster you go the more particles you have to push past.
Okay, I think I understand what you're getting at now.
A mass and the gravity-particle-grid exert a force on each other (action - reaction).
The mass forces the particles to spread apart. This creates an attraction, which reduces with increasing distance as the grid tries to draw other particles into the less-dense area.
Unfortunately, aside from being cumbersome, this model has basic problems with reality.
One example:
Either the gravity-particle-grid exerts a force on matter traveling through it, or it does not.
If it does, then you can account for the acceleration of objects due to gravity. However, at the same time, matter traveling through directionally uniform regions of your grid (a.k.a. probe in deep space, or planet moving around a circular orbit) would be slowed by the force exerted by the particles as it moves them.
This is not observed.
(Well, there is the Pioneer anomaly, but aside from having explanations waiting in the wings, not enough is known about it to justify throwing away physics. Yet.)
If your gravity-particle-grid does not exert a force on objects, it allows for the observed constant tangential velocity of orbital motion and the behaviour of space probes. But it does not account for acceleration towards a mass. Nor does this model allow for the mass to distort the grid in the first place.
As a third alternative, you could specify that the motion is only caused by a density gradient, that is, from one density to another.
Even if you do this, however, you will still need to account for how mass can distort the grid in the first place. And it likely has other implications I haven't thought of.