Hi MIgal,
In 2018, 06 - 20 Sept, I was in Switzerland and had great weather. I realize it can be different from year to year, but for me it was great. I wore a Tee or Polo shirt, and a pair of shorts for the whole two weeks, with the occasional sweatshirt as needed.. I had a backpack (separate from my main luggage) that went with me pretty much everywhere. In it, I had an extra sweatshirt, a pair of gloves, a ski hat, a compact rain jacket (which I never used), and a pair of sweatpants, just in case I needed any of it when I was hiking in the mountains. In my main luggage I had another sweatshirt and a pair of jeans, which I only wore once, (but didn't even need) when I visited Mt. Titlis.
As for the weather forecasts, don't even worry about them til you get there. I never once even looked at a weather forecast, other than the 'mountain cams' at the hotels, which are prevalent pretty much wherever you stay. As many folks mentioned, check a day or two before.
A basic rule of thumb is to not buy tickets for mountain excursions until the day of, pending the aforementioned 'cams' that most of the hotels do offer. There is plenty of nice hiking in St Moritz, but be aware that it is a ghost town (especially on Sunday) in Sept. Beautiful town, but again, pretty dead after the tourist season, though a lot of hiking to do. Try to see Mt. Corvatsch if possible.
In Zermatt, be sure to see the Gornagrat. Stunning scenery!! I saw it later in the day and saw the sun setting beyond the Matterhorn. Again, stunning.
In Wengen, well, so very much to see/do/hike around there.
I'd suggest going to St, Moritz from Zurich via Chur, then to Zermatt either on the main lines, or the Glacier Express (an eight hour ride either way). Then to Wengen and back to Zurich. OR the reverse. Either way would be one basic circle without backtracking.
Hope this many help you in some way. Have a great trip.
Regards,
Danielsan