Your link reveals this to be the name of a choir performing at a film screenung. However I can find no online contact for the choir. Perhaps it is a one off performance or it is an art piece?
The names of musical groups and art pieces are often enigmatic and unique. In this case all we can refer you to is the dictionary meaning of the words.
Since Walt Whitmans long poem "Leaves of Grass" it is not unheard of for music groups to incorporate the word Grass into their name. Perhaps weeds is a play on grass. And weeds are persistent and go where they aren't welcome: they are wilful.
But honestly you'd need to ask the singers what the name means to them.