It really depends on where you are in the country, as elevation can change up quite a bit, and hence the weather. I was in Norway before in early June, in the southern parts (Oslo, Flam, Bergen) and still needed a sweater in some areas. Up in the mountains (we took a train through them from Oslo to Flam), there was still snow. I would bring a sleeping bag for sure (nothing too hot though), plus a good rain jacket as being on the western side of Norway, there could be some heavy rains. That said, if the weather is clear, the sun will be out most of the day, or even 24 hour sun in the northern parts. I remember it being bright and sunny out at 10:30pm in early June, and that does definitely warm things up. Pack for weather between 5 and 25 degrees (Celsius) and you should cover all your bases.