Well, what do you mean by the rest of the universe having the Earth's gravity? Gravity is a force between two massive objects - Earth's gravity is the force that attracts us (and everything else) to the center of the Earth, but what would the universe's gravity be? In which direction would it pull us?

More importantly, if something in the universe were attracting us towards it, it would also attract the Earth as well. So both we and the Earth would be pulled towards this massive object, but in the meantime, we would continue to be pulled towards the center of the Earth as well, and stay planted on the surface of the Earth.

Even if the rest of the universe had earth's gravity, we would probably not float, since the earth has a strong enough gravitational pull to keep humans and other objects that are much less massive than the earth, from floating away.

The strength of gravity depends on the mass of the object divided by the square of the distance from that object's center. On the surface of the Earth, this is approximately ten meters per second per second (actually slightly less, but a first approximation). An Earth-sized planet elsewhere in the universe with the same mass of the Earth would have the same gravity.

It doesn't matter how much mass other things in the universe are when we're on the Earth because everything around us, including the Earth itself, is just as subject to their gravity as you are. You don't feel the gravity of the sun, for example, because the Earth is experiencing the same pull from the sun, and, as a result, is orbiting the sun just as you are. You notice the Earth's gravity only because you are standing on it and the surface of the Earth prevents you from falling deeper towards the center. An astronaut on the space station experiences over 90% of the gravity you experience on the Earth's surface, but doesn't feel it because the space station and everything on it are "falling" at the same rate - it is their horizontal velocity that keeps them in orbit instead of falling to the surface.