The land to water ratio
of earth is about 71% water and 29% land, so of the total area of the planet (200 million sq. miles) we end up with 58 million sq. miles of land.
The current ratio
is roughly 112 people per sq. mile (6.6 billion people/58 million sq. miles of land).
According to wikipedia
, the best total estimates of the entire population fall within 90-110 billion people. We will use 106 billion as it's the most trusted figure at the moment and wikipedia is never wrong.
So now that we have the statistics as accurately as we can get them (and if you don't like the numbers I picked, plug in your own. It's fun!), it's time for calculation:
For 106 billion people, you would need 950 million sq. miles to support them at 112 people per sq. mile.
This would lead to a total surface area of 3.3 billion sq. miles if we maintain the same land to water ratio.
Using the formula for getting the radius of a sphere from surface area, we find that the earth would have a radius of 16 thousand miles (as opposed to 4 thousand miles currently).
Now, in order to find the difference between gravitational force, we need to find the mass of our new planet. We will assume constant density of the two earths to be the same for simplicity. Currently, earth's density is 5.5153 grams per cubic centimeter.
The volume of our new earth will be 17.1 trillion cubic miles (compared to 268 billion cubic miles presently).
Using the density 2.29887732 x 10^16 grams per cubic mile, we find that the new earth would have a mass of 394.4 septillion kilograms as opposed to 5.97 septillion kilograms currently.
Using all of this, we find the acceleration at new Earth's surface to be roughly 39.7 meters per second squared. This would be approximately 4.05 g's or 4 times normal earth gravity.