Here some ideas requiring further discussion:
Attach a relationship property contributor class
or "fix" a set of property per OO association
One relationship type is split into two OO associations
or have the generic and the specific relationships in Neo4j but only the specific ones in OO. Each assoc is going to create 2 relationships.
For closed set of properties Neo4j recommends separate relationships. For open sets like weight, then properties make sense. How to host a weight in OO?