Without
gravity,
everything
needs to be
tied down
© NASA
As far as we know it does. One of the fundamental creeds of physics is that our fundamental laws of physics are independent of where you are. That does not mean that they are independent of what matter there is around you, so gravity near Earth could be different from gravity far from any matter, and it is – the curvature of space-time near Earth is different from that far away from any matter because the equations of gravity depend on the spatial distribution of matter, but the laws relating matter to gravity are the same.