Will my "the finalist certificate of the best paper award" be underrated if I co-chair a session at the same conference?
I would propose to put both points into your CV.

The interpretation you're afraid of is a bit far-fetched, and while some persons may indeed come to such a conclusion, I think most will not. Even for those who would think there has been an influence, I would argue that putting both is better than putting only one of them.
This is because they are in different CV categories, and thus people who evaluate your CV will in their mental checklist tick off both "won a paper award" and "chaired a conference session".