Just another way, using Cases, DeleteElements and Function:
Map[Function[{y}, Join[DeleteElements[y, {_, x_} :> x], Cases[y, {_, x_} :> x]]], list]
(*{{{1, 1, 1, 1}, 0.861155}, {{1, 1, 1, 11}, 0.512393}, {{1, 1, 1, 21}, 0.410614}, {{1, 1, 1, 31}, 0.351969}}*)