The weather in September here is not easy to explain.
It still can get very hot, but it can also can get very cold, especially in the nights. In every week there will be 1 or 2 days of rain, thats normal. But it depends on where you are. I live in Siegen, its the 2nd rainiest city in Germany.
Jeans will be perfect for any weather in September. Shorts for warmer days are ok, too. You will need some sweatshirts for the evenings and something like a jacket for the wet-days. Hope you won't have any rain!
And the rain here is not that strong like in Florida for example. Everytime when it was raining in Disney World i was like

until it stopped.
At the moment the weather is VERY bad here, so it only can get better! Its just raining and raining and raining.
Things you should do when you are over here:
- drink a Coke, it tastes totally different
- drink a glass of fresh water, you will be surprised how fresh it tastes
- rent a car and hit the Autobahn, you know, there are not much speed limits

- take a walk on an official way in the woods (signs on the trees will lead you), very nice landscaping in Germany
- go to a small village and look for a restaurant, often they have typical German food for low prices
- drink enough beer, you will miss the taste and the low prices
We don't have much tourists from the USA, so we are very happy when you visit us. Everyone 12 years or older should be able to tell you a direction or other easy things, because almost everyone learns English in school.
If you have enough time and you want to visit a theme park:
- Europapark, it's in the south of Germany, I think not too far from Heidelberg
- Phantasialand, it about 15 minutes from cologne
- Movie Park Germany (ex Warner Bros. Movie World), it's in Bottrop, in the north of the "Ruhrgebiet"
Hope you will have fun over here!
Ah I forgot something very important: If you want to use a taxi, I would prefer walking or taking the bus, because: It's very very expensive!