Waves need time to propagate, including gravitational waves. However you look at it, whether as a wave or particle or whatever quantum mechanics takes, gravitational fields spread only at the speed of light. In a relatively uniform gravity field, like earth or the sun, however, the effect is immediate because the gravity already exists. (essentially the gravity that has traveled already is affecting them, but is equivalent to the current gravity in a steady-state field.)
From the special theory of relativity, we learn that nothing can travel faster than the speed of light, and that includes the influence of gravity. From the general theory of relativity, we learn that gravity is the curvature of spacetime brought about by the presence of mass. So, for example, if the sun were instantaneously exterminated, this would cause a ripple effect that would further cause spacetime to "straighten out" from its previously curved shape, and those ripples, which just are the force of gravity, would spread out at the speed of light, but not instantaneously. This means, among other things, that if the sun were annihilated, we would neither see nor feel its absence for about eight minutes.
Anything that has mass possesses gravity. Mass does not appear and it takes a certain amount of time for its gravity to come into effect. It's instantaneous as once you have mass, you have gravity. When we jump, we are not defying the presence of gravity, we are simply applying enough force to overpower the resisting force of gravity for that time being before gravity's pull overpowers that of our applied force. In Physics, when we jump, our velocity never increases, it just decreases, proving that gravity is always there and is just wearing down our applied force.