Do followers get encumbered?

Solution 1:

Followers have a maximum carrying capacity, but they refuse to carry more rather than become encumbered.

More likely she's taking the normal amount of time to return "home", and the amount of time that takes just seems like a lot to you. For whatever reason, every NPC takes eons to walk back to their homes, and this is just normal.

Solution 2:

No, followers cannot become encumbered.

As mentioned in other answers, your follower has a maximum carrying capacity, and once they reach the limit, they won't accept any more items from you.

However, due to a bug/feature/quirk of the follower command system, you can overload them well beyond their maximum capacity. Even when they are at maximum carrying capacity, they will still pick things up off the floor if you command them to do it.

Using that "technique" your follower can carry an unlimited amount of weight and will not be hindered by it. They can still run at full speed and fast-travel with you.

Solution 3:

Once you reach maximum capacity on your follower, any item in your inventory that would overload the follower, is being grayed out so you cannot transfer it into their inventory anymore.

So no, they do not become encumbered, the interface simply refuses adding additional items.

The "Better not be things you possibly could not be bothered about." is a standard message that can come anytime, even is she is not carrying anything.

I would suggest that she rather got stuck somewhere due to a bug than because she was overloaded.

Solution 4:

This is most likely caused by the dragon born not being in the same cell as your follower. Your best bet of recovering her would be to follow the path from when you dismissed her and walk to her waiting location. That way the cell in which she is walking will be active and she will continue on her merry way.

If you are on PC and don't mind using the console you can just bring your follower directly to you. https://gaming.stackexchange.com/a/51628/8370