Here is a link to weather info:

( Kolkata ) Calcutta Weather 

 

Kolkata is at its most enjoyable period weather-wise from November to end of February. Although the tourist season runs from October to March, its still quite humid and hot in October and there are post monsoon showers which persist till mid or end October. March is also nice, but its gets pretty warm during the daytime.

December and January are perfect. There is little or no rain. There is warm sunshine that sets off the chill in the weather and early morning fog. The nights are cold but rarely freezing. If you can plan your trip, do so in December or January.

April to June, Kolkata is at its hottest. Its humid, the sun is blazing, and its almost impossible to sightsee during the daytime. After June the rains set in, and more often than not the heavy monsoon rain floods the streets and throws traffic out of gear. However, if you can brave the rains and the humidity, Kolkata during the monsoons is an unique experience. But be prepared to wade your way through water back to your hotel. 

All said and done, Kolkata is a unique city and more of an experience. If you do decide to visit, don't let the weather hinder you. 

 Culturally speaking, the Durga Pujas, a festival spread over four days, is a good time to visit, as that is when the city is at its liveliest. In 2012 Durga Pujas will be from 14 Oct to 17 Oct