Huh... I added a bunch of experience so I could level up to near max instantly. it ended up at level 92, but the results suprised me.
It did not change how much damage I did (maybe slightly? but not a lvl 7 to lvl 92 kind of difference). And the monsters did the same damage. But now i had thousands of HP. And even the basic healing items seem to be percentage based, so they gave me thousands of hp back.
I obviously haven't progressed, but the game seems to aim for the same experience throughout (...the kind that made me want to go max level), and they just give you more leeway to deal with damage. Maybe there are som story upgrades or something, but it certainly isn't level.
So general advice- dark souls this when possible, and just have a bunch of healing items. You don't progress by killing monsters, you simply don't fall behind.