GRAVITY...falling objects fall at the same speed in a vacuum? But surely heavier objects have more gravity and therefore would fall faster?

So, I have always understood that falling objects like a feather and egg fall at the same speed in a vacuum. However,the egg having more mass should have more gravity and therefore a stronger gravitational pull towards the earth. I read somewhere that falling objects basically don't have gravity, which seems... show more So, I have always understood that falling objects like a feather and egg fall at the same speed in a vacuum. However,the egg having more mass should have more gravity and therefore a stronger gravitational pull towards the earth. I read somewhere that falling objects basically don't have gravity, which seems silly. Doesn't everything have gravity? If everything has gravity and things with higher mass have more gravity then surely heavy things fall faster.
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