In [5]: def grouped_weighted_avg(values, weights, by):
...: return (values * weights).groupby(by).sum() / weights.groupby(by).sum()
In [6]: grouped_weighted_avg(values=df.wt, weights=df.value, by=df.index)
Out[6]:
Date
01/01/2012 0.791667
01/02/2012 0.722222
dtype: float64