It’s actually the other way around. Time gradients which form around masses cause different parts of other nearby masses to follow slightly different paths through space-time. The net result is than the masses’ trajectories deflect toward each other, giving the appearance of attraction which we call gravity.
More mass-density means a steeper time gradient, which results in stronger gravity.
[This video explains it nicely.](https://youtu.be/F5PfjsPdBzg)
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