My travel dates are flexible what month usually has the best weather?
Regardless which month " usually" has better weather, this year could be different, so I would not plan around that. Alpine weather is very changeable day to day and week to week. My first time in the Berner Oberland, late August/early September 2001, we had five days straight of glorious weather for hiking. I remember standing up on the little Männlichen Gipfel looking at the wonderful clear view, wearing shorts and a T-shirt. Ten days later ( around Sept. 12) my friends who were hiking the Alpine Pass Route faced over a foot of new snow near this same spot, and had to skip parts of the trail and take the train.
On subsequent trips, mostly late July and August, we have encountered both lovely days and rainy days. Usually a mix of both on the same trip. We were limited to theses days br school schedules.
You should just pick the time that works best for you and come prepared for anything. But lodging prices may be lower in September. That will be my choice next time, now that kids are out of college.
Thank you so much
"Best" is subjective. Statistically, September is slightly drier, but the difference isn't large enough that you could expect to avoid rain and clouds in one month over another. As Lola mentioned, the Alpine weather gods determine when it rains and when the sun shines and they're a fickle lot.
Now for temperatures, I would say September is a better bet, simply because your chances of hitting a heat wave are much smaller. Temperatures are usually very comfortable, just as long as you remember, this being the Alps, it could suddenly get much colder.
I was in Mürren in September 2014 for 4 nights. To amplify what Lola and Tom are saying about unpredictability, I had a day of clouds and poor visibility, two sunny and clear days (unfortunately one was shortened because it was my arrival day) and one day in between. I was very glad I stayed as long as I did; I would have been upset if all my time there was like my cloudy day. So, my advice is, whenever you go, stay as long as you can, to maximize your chance of clear days.