Question

What would happen if the value of G was twice as large

Answer 1

The gravitational force between any two bodies will be doubled 
also the gravity will become 9.8×2=19.6
our weight will also be doubled

Answer 2

This is a very inteteresting question!

Well, F_g = G Mm/r^2, right?

Where, M and m are two masses , r is the distance between them, and F_g is the force acting on each mass due to the other mass. So, F_g would double.

And the acceleration of an object with mass m (due to gravity alone) is a_m = F_g/m. Likewise, a_M = F_g / M. The accelerations of the masses would double, if G doubled.

Planetary orbital periods would be affected because the centripetal force would be twice as large. I.e.

m v^2/r = GMm/r^2

Now, m is the mass of the planet and M is the mass of the star it orbits. And, R is the instantaneous distance between the two. v is the instanteneous tangential velocity of the planet.

So, v = sqr. Root (G M/r) , so v would be sqr-root(2) times as bug. The period, which is approx. T = (2 pi r) / v would be reduced by a factor of sqr-root(2).

For the same orbital radius, the period would decrease by approx. a factor of 1.4142.

Now E_total = KE + PE

So E_tot = 1/2 m v^2 - GMm/r

Gravitational PE is a negative quantity.

So, E_tot = 1/2 m GM/r - GM/r = -1/2 GM/r

So, the total energy of a planet-star system would be doubled.

The internal energy of a normal star is something like U = -3/5 GM/R. Where R is the radius of the star and M is its mass. This would be doubled if G were doubled.

An object (say an astronaut) in free-fall above a planet would take half as long to reach the surface, if G were doubled. This is because his/her average speed would be doubled.

A lower limit to the time it takes for a cloud of interstellar hydrogen to collapse to form a star is found by assuming that the hydrigen molecules are in free-fall above the center of gravity of the (assumed spherical) cloud. This time would be halved for the same reason as the astronaut’s free-fall time. So, if G were doubled, we could expect stars to form more quickly and the star formation rates in galaxies to be larger.

Hope it helps.