It is possible to return any number of aggregated values from a groupby object with apply. Simply, return a Series and the index values will become the new column names.
Let's see a quick example:
df = pd.DataFrame({'group':['a','a','b','b'],
                   'd1':[5,10,100,30],
                   'd2':[7,1,3,20],
                   'weights':[.2,.8, .4, .6]},
                 columns=['group', 'd1', 'd2', 'weights'])
df
  group   d1  d2  weights
0     a    5   7      0.2
1     a   10   1      0.8
2     b  100   3      0.4
3     b   30  20      0.6
Define a custom function that will be passed to apply. It implicitly accepts a  DataFrame - meaning the data parameter is a  DataFrame. Notice how it uses multiple columns, which is not possible with the agg groupby method:
def weighted_average(data):
    d = {}
    d['d1_wa'] = np.average(data['d1'], weights=data['weights'])
    d['d2_wa'] = np.average(data['d2'], weights=data['weights'])
    return pd.Series(d)
Call the groupby apply method with our custom function:
df.groupby('group').apply(weighted_average)
       d1_wa  d2_wa
group              
a        9.0    2.2
b       58.0   13.2
You can get better performance by precalculating the weighted totals into new DataFrame columns as explained in other answers and avoid using apply altogether.