you might be overcoming more than just weight and friction in the plug.
the sticking tendency in the plug could have an initial higher (and varying) friction quality we sometimes call by the made up term "sticktion".
Investigate the addition of a lip or notch in the part to match a feature created on your gripper.
Sure customers are often dead set in not changing their parts to accommodate automation,
but the best solutions are often accompanied with small compromises. At least this has been my experience.
A...