How would the Sun's gravity affect us if we weren't in orbit?

So since we're in orbit around the sun, we are basically in free-fall. From what I understand, this means that we don't feel the gravity of the Sun like we do the Earth. Just like astronauts on the space station don't feel the gravity of the earth.

This got me wondering, how much would the Sun's gravity affect us if we weren't in free-fall. As if the Earth was being held by an invisible hand, and if that hand let go, we would fall straight into the Sun. Or if we had supports reaching to the Sun holding us in place, like a really really tall water tower.

Would the people on the side of the Earth facing the sun be lighter than the people on the opposing side? Would the difference be noticeable? Would people be pulled into the Sun, or would the distance make it's gravity be too weak compared to the Earth? This has been bugging me for a while.

Ok, let's add some numbers (if I did not make a mistake during calculation): If we are in our current position, the force between the side directed towards sun and the opposite site is at around $4\cdot10^{-8}\,{\rm N}$. Not so impressive? Ok, let's go further. If the distance is going down to $5\cdot10^8\,{\rm m}$, the difference force is going up to ~$1\,{\rm N}$. Still not impressive? Ok, let's narrow the distance down to $2\cdot10^7\,{\rm m}$. Then the resulting difference force is at around $17\cdot10^3\,{\rm N}$. Quite a lot and you are already worrying about that? Ok, then remember that Mercury is at a distance of $5.75\cdot10^{10}\,{\rm m}$, and there it is hot. So, I am sorry for the overweight ones who thought that moving themselves nearer towards sun would decrease the numbers on the scale: It would work, but only for a very short time.