Thanks for the app note, cjands40. I'll come back to this once I know where the final installation place for the weather station will be and what cable length I will need.
For now I have installed the SHT very close to the Arduino and it works now. I'm really happy that it wasn't a broken sensor as that is so far the most expensive component of the whole project... 
At least for now I don't need to wonder how I'm going to measure humidity from inside my watertight temperature sensor box... 
And because a picture says more than a thousand words, here's a screenshot of my current graphs in Cacti. Then I'll get out of this hijacked thread and start my own for the next issues...
