Visiting during first week of June? Is the weather very bad, should I just postpone it to a later date?

Currently in Delhi, planned to visit Kerala and cover all the must-see places in the next 2-3 weeks (the typical itinerary involving Kochi, Aleppey, Varkala, Munnar, etc.). Couple of Indian friends (I am not a local) suggested to not go ahead with it since monsoon has started and weather may be bad (AccuWeather says the same). Kinda feeling dejected now, but wanted to know some opinions from locals before cancelling my plans.