Would a 90 kg object jettisoned from an aircraft create a detectable movement?
Yes

It's not just weight, it's also aerodynamics. First let's assume that the aircraft was trimmed slightly nose-heavy (no passengers), therefore it's trimmed slightly "tail down" anyway

When the stair was first opened, it would have been held partially closed by the airflow under the fuselage - it's not heavy enough alone to extend fully against a 100 knot wind.

There was then a two-part change from Cooper leaving the aircraft - one of him walking down the stair, pushing it into the airflow and acting much like the elevator.

When he then jumped, the loss of his weight at the very back of the aircraft, along with a presumed "push" against the door, pushing it further into the airstream, would have simultaneously jolted the tail up, then reduced the weight at the very back of the tail "lever".

90kg doesn't sound like very much, but when it's at the very, very back of quite a long lever, and when combined with the airstair, the results seem perfectly reasonable and, indeed, were proven by the FBI.