Oh, I know my mistake. I have to create a one-to-many relationship instead of a many-to-many. Then it works :)

Okay that's not the solution :/ I definitely need a many-to-many-relationship because else I have the following problem:

If I want to get all researches and I eager load the research_costs table (which is a one-to-many relationship between it and researches) I get the costs for ALL levels within the array of ALL researches. But I need to have the costs only for the specific research, other wise it would be redundant.

In other words, I would like to access the costs like this

$researches[0]->research_costs

instead of

$researches[0]->research_costs[0]

I hope you understand the problem. Hence, I need to use a many-to-many relationship like explained above but it doesn't work :/