Just repeating this here so that people can avoid this misconception. Gravity is weak! Its only strength is that it operates over VERY large distances. And I mean VERY large, the entire cosmos. The other fundamental forces tend to operate at the subatomic level where they're ridiculously strong. They can and do operate at the macro level but with difficulty.
Actually gravity is ridiculously weak. Take a paper clip, hold a magnet over it. A tiny fridge magnet if you have one. Here's the thing. Your little tiny magnet exerting just a tiny fraction of the electromagnetic force if you put it close above the paper clip, the paper clip (assuming it's metal and not plastic coated) will jump UP to the magnet, when it does that and stays there, your tiny little fridge magnet has just overcome the gravitational force of the ENTIRE PLANET.
That's how weak gravity is and accelerating even in a normal plane is overcoming gravity and now operating stronger than gravity of planet earth by a few times. In space you could do that even more. So strangely gravity in space of an accelerating ship would be MUCH stronger than planet earth.
Hope this helps.
Ex-astrophysicist, currently a teacher.