Curving something towards the center is not Newton, he did not provide any explanation for the force of gravity, only a mechanical description of it's effects.
Curving spacetime towards an object means, simply, that objects moving through the spacetime near that object will tend to get closer to said object.
As I'm fond of using this description lately, see if this way of thinking helps explain the effect better.
Go into your bedroom, assuming you have a sheet on your mattress, grab a bit of the sheet and twist it up in your hand.
Notice how it stretches the rest of the sheet?
While holding the first part, grab another part, and attempt to ball the sheet up in your hands.
Rather quickly you should feel your hands being drawn together.
Stop crumpling the sheet up with one hand, and maintain that section as it is.
Now ball up the other further, what happened to the one you stopped crumpling?
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