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We have discussed several times having a pluggable belief calculus. This could achieve what you want in a general framework. This might operate by tracking the identity of each tuple supporting a query, then going back over those tuples and applying weights using a customer specified formula to compute the aggregate score for each solution. #neptune-interest if you want to discuss use cases.
You can use things such as shortest paths with Neptune Analytics to find a minimum cost path. If your graph is just edges and weights, some flavor of graph algorithm might give you want you want with an appropriate semi-ring. Again, #neptune-interest to discuss.
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Are you thinking along the lines of precomputing the impacts in real time too, or could they be stored as edge weights between the nodes? A bit like (A)-[:IMPACT {weight:0.5}]->(C)