Question

What would happen if the moon were twice as big

Answer 1

The force is the same force the moon pulls on the earth is the same as the earth pulls the moon

Answer 2

The universal gravity formula is F = G(Me)(Mm)/r^2. Lets use this formula to help us calculate what would happen if the Moon was twice as big.
Mn = new mass = 2*Mm
Fn = G(Me)(Mn)/r^2
Fn = G(Me)(2Mm)/r^2
Fn = 2*G(Me)(Mm)/r^2
Fn = 2*F
So 2 times the force it was before. The force should be the same, but you never know the moon and space as well know it can work in very mysterious ways.