I found a fantastic weather page on the SMHI (Swedish Meteorological and Hydrological Institute) website.
It gives a great deal of weather information for Stavsnäs, specifically temperature, winds, and precipitation, in an interactive format. You can look at tomorrow's weather hour by hour, or look forward 10 days.
The weather in Stavsnäs is pretty close to what we expect in Aspö, but not perfect. I remember when we were assembling the house in August 2008. We had sunshine overhead every day but a line of clouds over the mainland, which never made it to us.
It's also possible to see the Sandhamn forecast to get more of an island flavor, but it appears to be pretty similar to Stavsnäs, at least over the past week.
Either way, this is pretty cool, and I will probably spend a lot of time looking at the weather, wishing I was there.