I've had Annekka as a follower since around level 20, I'm now at level 44, Annekka's combat and sneak have definitely gotten better, early on her sneak was poor and the enemies would detect her, now we stand together in sneak mode and draugr's walk withing feet of her and not notice as long as neither of us are moving.

I've also been letting her do combat while my character stays in hiding, the more I've done this the better she has become, certainly seeing a lot more finishing moves from her.

So, are followers leveling up independently if you just let them do their thing?

PS, this is not a complaint, it's an aspect I'm really enjoying.

I heard they did not level up with you and that their stats are set when you first meet them.

This is something I also read, but it does not appear to be that way, Annekka has epic glass armor from head to foot, but nothing to help her sneak, no amulets or rings.
She also just gave a dragon priest quite a pasting, she did not beat him but certainly wiped away a lot of his health before submitting, then I finished him off.

I'm not sure it's set in stone. For example I've had Marcurio demolish everyone while J'Zhargo is getting rocked. I also read that releasing the follower and taking them back brings their level even with yours.

Not sure though, all speculation.

Hmmm... Every time I go out with Lydia or Jenessa, they take one or two hits before going down. They definitely do nit seem to be leveling along with me.

BTW-I have equipped hem both with great armor and weapons, so that's not the problem.

They level up when you do, but there stats remain fixed in the state they were in when you first entered their cell. So if you meet Lydia at level 3, she'll have level 3 stats for the rest of the game. If you meet Jordis at level 40, she'll have level 40 stats (500+ health, 100 onehanded skill, etc.) for the rest of the game.