Is there greater gravitational force the higher up you drop something?

No. In fact, the further you are from the bottom of a gravitational well (Basically, the center of a planet/star/etc.) the lower the gravitational pull will be. Were you to drop something from extremely high up, it would encounter increasing gravity as it fell down. This is why probes that we send into Jupiter's atmosphere get destroyed- the gravity exerted on them by Jupiter gets higher and higher until they are destroyed by it.