Pretty much nothing. The overwhelming gravitational effect that we feel is from the Earth, and that'd remain the same no matter what happened to the Sun.
What would happen next if sagebrush is disappeared frrom a desert?
You would die.
You would die.
if the oxygen
If gravity suddenly disappeared, the moon would fly out into space in a straight line. If the moon suddenly stopped moving it would fall straight into Earth.
Everything would die
What would happen to the earth if the sun's mass (and, thereby, its gravity) suddenly went to zero? The earth would continue moving in the direction it was going when the sun's gravity disappeared. It would depart the area on a tangent to its original orbit and head off into space. There would be dark days ahead.
There would be no bees to pollenate the flowers.
In zero gravity, buoyancy would not be present as there is no gravity to create the force that causes objects to float in a fluid. Objects would not experience an apparent weight loss or loss of buoyancy in zero gravity.
This cannot possibly happen, so asking what would happen if it did happen is an exercise in stupidity.
life would follow
Your mass would be unaffected, it is simply to do with the atoms in your body. Your weight would be reduced to zero as that is simply how much your body is affected by gravity.