Sidekiq not deallocating memory after workers have finished
Mike Perham who wrote Sidekiq addressed this here: http://www.mikeperham.com/2009/05/25/memory-hungry-ruby-daemons/
tl;dr version: MRI will not give the memory back, the most you can do is control the heap, and to do that, Ruby Enterprise Edition was suggested.
Don't know that any of this helps, but that is the situation - straight from the horse's mouth.