In Weaviate nearText search, one will be able to control results either using certainty or distance. For example, one can set certainty = 0.75 ensuring that not-so relevant results are not included.
Is this possible in Weaviate Hybrid search? I can only see score as part of the output additional information but cannot use it for controlling the results (e.g., a score of > X only)
No, it is not possible to do that. You will have to implement that as a custom post processing step. Feel free to raise a feature request at the weaviate repo to have this be done inside weaviate itself.