Weather wise which month would be better to visit Bernese oberland, June or July?

"Without any obstruction". You'll need to build some flexibility into your schedule as even cloudy weather without rain can impact your mountain and meadow vistas. Check the historical weather data on a website like wunderground.com looking at days of sunshine and precipitation. However the only way to try to maximize your chances is to be nearby and plan to go up to a mountain area when the local forecast is only a few days out. Even then you may get clouds and sun alternating much of the day, which adds to the drama.

We based ourselves a few hours away from our mountain experience a few years ago and only booked a hotel in Zermatt (could have been Lauterbrunnen, Murren, etc.) when we were fairly confident the weather would be clear for part of the day.

I went july 2017.
It did not rain; the averages peak in the end of May - June.
Also the views are better the higher up in the early morning before the clouds roll in

I've been in June 3 times and the weather was beautiful. We have always stayed in the Lauterbrunnen valley for 4 or 5 days each trip and have only had 1 rainy day. Having said that - there has been a little snow on the trails when we've been. Last time we were there we arrived on June 17th. We had planned on doing the hike from First to Schyngge Platte. It was technically still closed so we decided to to part of it from First to the Faulhorn. Well - long story short at the Faulhorn we decided to go the whole way, but ended up NOT being able to finish it and going down a very steep valley which was not much fun:( We're going back next year hoping to complete this hike. We plan on arriving on July 9th staying for 6 nights this time. Unless they have a crazy amount of snow this year we should be good:)

If I had a choice to either go in June or July, I would definitely wait to go in July. While the weather can never be guaranteed, you have a better chance of having good weather in July. We arrived in Switzerland July 2nd this year and stayed for 2 weeks. We had glorious sunshine every day. It was just beautiful! Now, my previous trip to Switzerland was in June 2011 (around the second week) It rained every day. In fact, when I looked out my hotel room we saw nothing but fog/clouds until the day of our departure when finally Mont Blanc was in view. One day of actually seeing the mountains - so disappointing.

It is not cheap to travel to Switzerland so hang on a couple more weeks and book in July (but go before the schools get out in Europe which is usually around July 20th).

I've been there in both months. I've had rain and sun in both. Not sure there is a significant advantage rainwise in waiting for July.

One advantage that July does have is that you are less likely to encounter hiking trails closed due to lingering snow pack.

I prefer to go in July. Most of my favorite hiking trails don't open until early July when the snow has melted and drained and the maintenance has been done. Before that the cable cars that take you up there are still closed.

Also, in July, the alpine flowers bloom in profusion.

Allow extra days to see the vast vistas, since it rains or clouds up often. Usually the clearest weather is in the mornings.