I seem to recall the assimilation was rising when he was occupying that first dungeon - a skeleton dungeon at that. And he came close to loosing his own consciousness from it - becoming part of the dungeon. Earlier it referred to dungeon assimilation but now just says assimilation. But I also don't know the significance here.
Honestly I was hoping he'd get killed by a surprise attack and resurrect again with a chance to grind those guards again.
I think assimilation has to do with how close he comes to losing himself and becoming a true monster. It's possible that as the rate goes down, he gets closer to returning to what he was originally, which I assume is a human. I mean, where did his bones come from? They're human bones. He was once a human being. Perhaps he's being given a chance to live life again. That'd be pretty cool if that were the case..
For those who are wondering about assimilation it affects his mental state making him turn into a mindless mob once he crosses the threshold as observed when he stayed too long in the dungeon with blondie. So the lower the better.
^this
Also it goes down when he reincarnates and progresses enough to change/achieve something(creating a save point?).
My guess is the Assimilation is how similar he is to his original self that reincarnated in the first place. It may represent the %possibility of failing to reincarnate (tutorial mode?).
Or perhaps it is an indicator of the proximity to his original world line and 0% represents a new world line (steins gate?).