This problem was discussed at Steam back in 2016 without beeing solved and still exists:

If you play in coop (local, 2 computers in same room, not in online mode), the host gains more XP/levels than the client!

Me and my GF had hell of fun with this game (it's awesome!), but she's really annoyed by the level mismatch because I'm 2 levels ahead, close to the end of the game: All dropped loot is my level now, and she can't use it.

The wierdest thing about this is:
If she keeps parts for later usage that are all or mostly green in their stats (so, "better" than her parts), and she finally reached the level required for the new ones, the stats are now red in most cases; which would mean the item got worse?!! I have no explanation for this.
We even wrote down some values of an item and checked them before and after her level-up, and the numbers in the description of the item were the same. However, the stat comparison table (in advanced view) did show that the item got worse since we last checked it; like: DPS was +50 before and +5 after.
Yes, she leveled up in between. But her character stats should affect BOTH of the items, not only the one she's actually using. Right? So shouldn't the new item still be much better than her old one?
Since we noticed that, she just shows me her loot, sells what I don't want to use (95%), and prays that the merchant has got something for her. So, the merchand and the Chimera are her only options to get new stuff; which is ... [enter bad words here]

This all started somewhere around level 50, when we first noticed the XP mismatch.
It wasn't a big deal back then, she quickly leveled on par. But it got worse soon.
I was even staying in the background to give her more chances of kills, esp. with bosses.
But that worked in no way: My XP gain did slow down a bit, but I still leveled up way before her.

As mentioned on top, the problem seems to be around since 2016 when a couple of players reported the same issue on Steam. It's unsolved.

Hopefully, somebody here has an idea ...

Belushi

Update & Workaround:

I was not aware of the fact that the server does NOT save the journal/quest progress, as it usually is the case with other games (like Titan Quest). Actually, the progress is stored in each player's character - which is also true for the client's character!

This means: My GF (who was the client before) can start a multiplayer game with her co-op character and I can join her game, with all quests, stats and items set correctly. Actually, you can swap server/client at any given time, solving the problem - because now she gains a bit more experience than me until she is on par or a bit ahead of me. Then we swap server/client again, and so on.

This is a bit annoying, but it WORKS - and usually has only to be done every second or third session.

I hope this is helpfull for somebody!