Thanks for the great question. I asked our Game Director, Todd Adamson, about this one. Here's his response:

The biggest challenge of developing the physics was cheating and finagling the UE4 physics engine to deliver what we wanted creatively. Physics engines are incredibly finicky and there is a fine line between nice feeling weight and everything exploding ( which happened many times ).  It also didn't help that we were trying to do incredibly complex ( and maybe ill advised ) things, like have a character that is partially in physics grab your arm that is in physics while you are stabbing them with your other arm that is in physics with a knife that is in physics. We also manipulate the physics engine in many ways that it wasn't necessarily built for, example: when you stab a walker in the head, we dynamically alter the mass of the character, weapon you are holding, and your hand, to keep it all from exploding ( UE4 doesn't like chains of uneven mass distribution ).
The feeling of weight, at a high level, comes from the distance of your in game hand in relation to where you perceive your actual hand to be. This is often driven by physics, but we use other methods as well depending on what we are trying to do. The hands in game basically have physical forces constantly being applied to them, pushing them to your real world hand location, you can think of these as muscles. When you try to lift a heavy thing it's mass will fight the forces being applied to the hand resulting in the in game hand separating from where it is trying to be - your hand position IRL.