In [353]: dff = df.dropna(subset=['Value'])
In [354]: dff.apply(lambda x: np.ma.average(
np.ma.MaskedArray(x, mask=np.isnan(x)), weights=dff.Value))
Out[354]:
A 1.282629e+04
B 4.295120e+04
C 4.652817e+04
D 4.545254e+04
E 4.601520e+04
F 4.212276e+04
Value 3.260246e+09
dtype: float64