How do I create a new column from the output of pandas groupby().sum()?

You want to use transform. This will return a Series with the index aligned to the df so you can then add it as a new column:

df = pd.DataFrame({
    'Date': ['2015-05-08', '2015-05-07', '2015-05-06', '2015-05-05',
             '2015-05-08', '2015-05-07', '2015-05-06', '2015-05-05'],
    'Sym': ['aapl', 'aapl', 'aapl', 'aapl', 'aaww', 'aaww', 'aaww', 'aaww'],
    'Data2': [11, 8, 10, 15, 110, 60, 100, 40],
    'Data3': [5, 8, 6, 1, 50, 100, 60, 120]
})
​
df['Data4'] = df['Data3'].groupby(df['Date']).transform('sum')
df

         Date   Sym  Data2  Data3  Data4
0  2015-05-08  aapl     11      5     55
1  2015-05-07  aapl      8      8    108
2  2015-05-06  aapl     10      6     66
3  2015-05-05  aapl     15      1    121
4  2015-05-08  aaww    110     50     55
5  2015-05-07  aaww     60    100    108
6  2015-05-06  aaww    100     60     66
7  2015-05-05  aaww     40    120    121