Weather can be variable, even on the same day. When the ship stops close to a glacier, you're going to want to wear heavy clothing so you can be on an outer deck for a long time, to watch the glacier and other scenery. In port, it may be cooler in the morning and then warm up later. Best thing to do is bring clothing you can layer, such as short sleeve shirts, cotton sweater, sweatshirt, rainproof outer wear. Layering is also the most effective way to trap body heat and stay warm.
We cruised to Alaska in mid-July some years back, and loved it. You'll have enough light at 11pm to read a newspaper on an outer deck.