I have to say I’m not the best at replication yet however, I have replicated all of my game so far. Including the replicating picking up Physics objects for both client and server. Basic things to check are…
In your MarbleBP properties have you got Replication box ticked? And Replicate Movement ticked? Also you mention a Drag and drop feature? Is this in the CharacterBP? If so have you added Custom events to run this logic on the server?
It might help if you post your characterBP for your ‘Drag and Drop’ feature.