Antigua should be seen as a year round destination despite very recent huricanes such as Irma devastating Barbuda and disturbing Antigua.
The actual season in Antigua runs from late November to the end of April thanks to Antigua Sailing week extending it. It is also more expensive to visit during this peak season.
An expensive blip occurs for Carnival each Summer time FOR FLIGHTS but it's a fun time to hit the island for many. The season falls outside of hurricane season but perhaps more importantly coincides with the northern hemisphere winter. Canadians and Americans fed up with the snow and harsh winters like to take a Caribbean Holiday and Antigua is well served by flights and operators such as Sunwing are opening up the island to more new value routes.
Out of season there is blip for the school holidays when Antigua also excells at family holidays.
The season is slightly cooler than in summer and has less rainfall. If you want more detail then look here. Average temperatires are good year round and out of season you might like the odd cloud and shower. You will normally still get enough sun for a nice holiday.
Some parts of the island almost shut down fully in the Summer however; and if you like to party you will need to find the local nightlife. Jolly Harbour has the best all round nighlife in terms of places staying open. The normally rambunctious falmouth and English Harbour shuts down outside of the season. Prices drop but never really really low and prices will never compare to the Dominican Republic and Mexico deals you can find. Antigua is not like that.