How should I set up 2D animations for weapons in Unity?

I have a character composed of several sprites (legs, torso, head, arms). The character has the ability to pick up weapons, which are of varied types.

Each type of weapon has its own animation (sprite sheet). Ideally I want the weapons not only to animate themselves, but also affect how the player is animated (e.g. lean back when swinging sword).

Here's how I'm thinking of setting it up right now:

Player has an animator controller with states for Walking, Attacking, Idle, Flinching and this controls all the body parts.

Main questions: - How can I incorporate jumping in this? - How can the weapon animations have control over the rest of the body?

For having different weapons I am thinking of adding different states per weapon type, but I don't think that's a great way, especially when I start adding combos.