How to make armour fit to your character mesh via socket and scale automatically?

I am having issues where amour does not fit correctly around my character mesh, how do I fix this?

You edit the model. Its the only appeopriate way.

Some games have it so that armour automatically adapts to your character size, how do they do it?

The only way to do that reliably would be to use the same modifiers on the armature as on the character.
Be they bones (ARK used to do it that way) or Morph Targets.

You would still get some clipping artifacts at times. In zones like elbows/armpits particularly.

And the mesh itself needs to be properly setup for it, obviously.