I've noticed that Lydia won't "ready" her weapon when I do. I've been using her like a pack mule. Instead of the normal transfer of items through "I need to trade some things with you" dialogue I've just been having her pick them up off the ground as I read somewhere that companions can carry more that way. When she gets over-encumbered will she no longer fight?

Atleast you still have Lydia, I've lost her due to a glitch.