Something the size of the Moon.

Gravity as a force is not inherent to an object, but is the attraction between two objects. Anything launched into space alters gravity, otherwise it could never achieve escape velocity.

Anything launched into space will decrease the force of gravity felt on the planet’s surface by an infinitesimal amount. If the object remains in the Earth’s orbit the effects at a great enough distance will be zero. Material launched into space is more than compensated for by the material that falls constantly onto the earth in the form of meteors and meteorites.

Tons and tons and tons. And it would all have to be in the same segment of the sky, above the same spot on Earth, in geosynchronous orbit.

It would have to cause a significant reduction in Earth’s mass (~6×10e24 kg). I would guess that a disappearance of 6×10e22 kg (1%) would make it noticeable.