I'm sorry I hit the enter and the thread was born before I finished the title, so now some rushed thought only: There are those stories of the giants in the Bible, in greek myths and in many legends across the world, we have fossils of giant animals and plants, we have buildings from out acient past that are too heavy and too big to be made right now - what if before the great flood the gravity was lighter?
Is it possible?

Little more explanation to the previous post:
I have read many old legends involving grand changes of the Earth, some of them from various places around the world are telling different version of what seems to be the same story: the sky fell down and there was the great flood and everything changed.
Just yesterday read this thread about possibility that Earth once didn't have moon.
Maybe all of it is connected?
Maybe Our Earth was once moon free with lighter gravitational pool, that allowed plants and animals (and who knows, maybe humans too/) to grow big, but than something happen in our solar system something which caused all those changes, including changes in Earth crust...
Maybe Earth got a moon, maybe changed orbit around the sun and maybe changed it gravity too...
just some fuel for thought....

Or maybe a massive body passed near to Earth in the past and the gravity from this other body "pooled up" Earth's seawater to the side facing the passing body. Thinking out loud...

Maybe this happened around the time we got our slow angular wobble... (precesion of the equinoxes)

This is highly speculative place for out of the box thought, the current moon theory has as much evidence as the story of an alien intervention, we simply don't know.

As for the growth of the body mass of animals and its connection to the oxygen level well, I think oxygen level was not an cause, but rather an effect of different quantity of giant plants...

As others have posted on here, gravity comes from the mass of an object. The greater the mass, the greater the gravitational force of that object.

In order to change the Earth's gravity, you have to add mass, and as it has been pointed out, the material the Earth does collect only adds mass in a very gradual way that would take much too long for your idea.

The only way for your idea to work, is if the mass is added very quickly, in large amounts. That would be large impactors with the Earth.

However, that would be a very bad thing. For example, the asteroid that hit the Earth 65 million years ago was only just under 7 miles wide, so it's mass was actually very insignificant when compared to the Earth's mass, in that, after it's impact, it would not have changed our gravity enough to be noticed.
But the effects of that impact certainly were since it wiped out 60 to 70% of life here.

In order to have much more mass, you'd have to have literally hundreds of that size asteroid hitting the Earth. And if the effects of just that one were so devestating, you can imagine what hundreds of them at a time would do.

Or, you'd have to a single very large impactor measuring in hundreds of miles, if not over a thousand miles wide.

However, if that were to happen, it would be very, very bad. Most of the Earth's crust would become molten from that type of impact. Absolutely nothing on the surface would survive or remain. Even if it happened today, the only thing remaining of us humans would be our satellites in space, the junk we left on the moon, and the probes in space. Everything else on the surface of our planet would be gone.

So there is no easy way to increase the Earth's mass and hence gravity quickly (in geological terms) without destroying everything that is here.

Originally posted by Heliophant
Or maybe a massive body passed near to Earth in the past and the gravity from this other body "pooled up" Earth's seawater to the side facing the passing body. Thinking out loud...

Maybe this happened around the time we got our slow angular wobble... (precesion of the equinoxes)

edit on 28-2-2013 by Heliophant because: (no reason given)

You may be on to something with some "Body" passing close to earth.

This is a Google Earth snap shot of the area between South America and Antarctica. If depicted correctly, not only did a "body" pass by very closely, it was in contact for some time. I am suggesting that something spherical approximately 300 miles in diameter did just that. It appears to have left its track. My guess is this feature is between 70 and 80 million years old.