I know when you join with a companion they give you their perks. but do you give them you perks? Or do your perks not effect them at all?

no why would they?

Well, there is at least one that does seem to be shared - Animal Friend. Taking that and having a companion will result in the companion not initiating combat with or being jumped by every gecko under the sun. I am not positive about any others though, and really have no desire to test if they get Light Step (I believe they do not).

Thats because that perk changes your relation to the animals faction, IIRC companions use your "faction".