Your question is not entirely clear, I'm not sure what you're asking... here's an attempt to answer:
The Earth orbits the sun, while the Earth also rotates on its own axis. Think of it like your friend spinning a basketball on their finger while walking around you in circles.
Relative to the Earth, we are not moving, so there is no increased mass for any velocity that we have relative to the Earth.
The rotation of the Earth on its axis actually causes us to lose some mass (very, very small amount) due to inertial forces, that is, the Earth is trying to push us off of it- to reference the basketball example, imagine the basketball was very wet, as your friend spins it, some water flings off the ball.
The orbit of the earth around the sun, will cause us to both become pressed against the Earth (while on the sun side) and pushed away from Earth (on the dark side) due to inertia. These effects are ... VERY VERY VERY VERY small and hardly even worth mentioning.
We continue to orbit the sun because spacetime around the sun is curved - gravity. http://spaceplace.nasa.gov/how-orbits-wo…