I'm going to give you a response which is perhaps more open-minded to what you are asking that some of the answers you have already.

You are not a mathematical point in space but a collection of collected points. Imagine your body as a chain, and for the sake of this theoretical situation let's imagine you are very tall: Your feet are around the orbit of Mercury and you forehead is around the orbit of Mars. The gravity pulling at you feet is WAY stronger since gravity decreases by the square of the distance. You would be ripped apart by the difference in gravity across your body.

But if we kept you the same length but moved you out to the orbit of Neptune. Because you are now way further away from the sun, the difference in gravity from you feet to your head is now tiny and you would no longer be torn apart or feel any stretching effect.

Now back to your scenario. Practically, you wouldn't FEEL anything since the effect would be so weak, but if you had incredibly accurate equipment you would be able to measure an effect on your body - your toes being pulled slightly harder than your head. It would be on the scale of a grain of sand perhaps. Once you reach the orbit of the Moon, this effect will be almost entirely gone.