June-July is the warmest weather- ON AVERAGE. No guarantees on Alaska weather. Coldest is Sept. Probably most sunny in May.
Frankly, you are setting yourself up for disappointment if the weather is your factor in planning an Alaska trip. I would instead suggest you consider what activities you are looking for and plan your trip around them?
Well Im very thin and get cold easy, so that is why Im looking to book in the warmest months. I can deal with rain and a certain amount of cold (Im from Chicago) I want to go whale watching for sure and maybe land on a glacier with helicopter.