We have sailed to Alaska in early June and late September. We were lucky to have reasonable weather both times, apart from heavy rain in Juneau in June. We actually preferred the early June sailing as there was still snow around, particularly on the White Pass train trip. Also the approaches to Glacier Bay, as I remember were all snow covered in June. On the September trip I did not think the scenery was as atmospheric, and somehow not as beautiful. Although Glacier Bay at any time of the year is just amazing. One advantage of going in late September is there are a lot of bargains to be had in the shops. We bought some beautiful local greeting cards in Juneau and Ketchikan.
Having said all this however, I would happily jump at the chance to go back to Alaska at any time of the year!