I saw that you posted the same question on the FuelPHP forum, so here I will try to give you another solution.
Why your relation needs "id, user_id, liked_by"? I think you can improve you database modifying a little your tabel.
Reading your question I think you have a structure like that:
// USER TABLE
id
username
... something more
If you create a table named "LIKE" you'll have this situation:
// LIKE
id
created_at
modified_at
... something more
So now you can create a many-to-many relation with a table named "users_likes" with:
// USERS_LIKES
profile_id // it wil be related to the user_id, is the user's profile being liked
liker_id // it will be the user_id of the user that likes the profile
So if you want to retrieve the number of the like you'll have all the information in the current user model or in the profile user model.