How to attach a single node multiple times to an entity (e.g. badges)?
Somehow it kept slipping my attention, I was probably focussed too much on specific ideas, but as it turns out, there is already a module for that, it's simply called Relation.

It's not that straight forward to use (imho), but it essentially creates relations between entities. The created relations are also entities and thus fieldable. By creating a relation type (A [owns] B / B [is owned by] A), I can add a custom field "amount" which holds the information how many Bs are owned by A.

The result (one custom view block added plus a single line of CSS) looks like this.