First let me remind you, if I may, that the force of gravity is the attraction that exists between any two masses. We feel it as "weight", but it's expressed mathematically as the force of attraction between our body mass and the mass of the planet beneath us.
If you placed two cricket balls on a flat surface, not touching, there would be an attractive force between them. To be sure, it would be negligible, but mathematically it would exist. We can calculate it, in fact.
Gravitational constant G = 6.673 x 10-11
m, Mass of each ball 0.163 kg
d, Distance between their centers (say) 0.12 m
f = G mm/d2
f = 6.673 x 26.5 x 10-14
/1.44 x 10-2
f = 12.28 x 10-11
Of course, the force of attraction between a cricket ball and planet Earth is not negligible at all. It is the ball's weight, or its mass multiplied by the acceleration due to gravity.
0.163 x 9.8 = 1.6 newtons
We could calculate the atraction between a cricket ball here on Earth and the planet Mars. It would be even more ridiculously negligible but, again, mathematically it exists.
Expat rides a hobby-horse:
If you're American, you've been taught that an object of mass 10lb also has a weight of 10lb by definition, and isn't that convenient? Yes, it's convenient but it's also confusing. It accounts for the misunderstanding of the difference between mass and weight in the average American mind.
All right, enough of the Grade 6 physics. Let's think about a flat Earth. Such a concept is usually depicted roughly thus, an obtuse cone:
Consider a man standing in the center:
That's him, standing proudly erect, with the force of gravity as a vector acting vertically. It's perfectly possible for him to feel the same gravitiational force as he does on a spherical Earth.
But now, get him to walk half way to the edge of the flat Earth.
If he tries to stand vertically, he's got a problem. Consider the planet beneath him as two pieces, separated by the vertical line. The right piece is way larger than the left piece. It is therefore also way more massive, and exerts much greater attractive force on our man than does the left piece.
The gravitational vector is not, in this case, vertical, and our man is going to have to lean left to avoid falling down.
I've attempted to draw the vector such that it bisects the flat planet.
Now let the man walk all the way to the edge. The gravitational vector is now almost horizontal.
This model may be flat, but to its inhabitants, it would seem like a rather steep-sided bowl.
Of course, we don't need any more reasons to refute the claims of flat Earthers. We already know that the Earth is a solid sphere. But if you should happen to find yourself having a beer with some of those maniacs, try telling them about the gravity vector on their hypothetical planet.