The concert will be held despite/in spite of rainy or sunny weather Or the concert will be held whether it is rainy or sunny

The main error is in "...is will be...". The rest is a matter of style, I think. I have seen sentences like "The concert will be held rain or shine" in printed form. It is a terse style but there's really nothing wrong with it per se. In fact, I think the trend is to favor such compact and to-the-point style more and more.

The concert will be held, come rain or shine.