puppet

Where it comes from

Puppet developed from Middle English popet and French poupette, a diminutive meaning a little doll. The French family descends from a Latin form related to pupa, girl or doll.

How the meaning developed

A small human figure became specifically a figure moved by strings, wires, or a hand. Because its apparent actions come from an unseen operator, puppet was quickly extended to a person or government controlled by someone else. Pupil and probably puppy are distant members of the same little-child and doll family.

In use

A puppet moves, but someone else controls it.
Calling a person a “puppet” makes the same accusation: someone else is in charge.

French “poupette” meant a little doll. English “puppet” became a name for a figure moved by strings or a hand.
That dependence on an operator explains the figurative meaning: a person controlled by someone else.
No actual strings required.