Marking the entire group if condition is true for a single row

For improve performance dont use groupby, rather get all WeekNum with at least one 1 and then select values by isin, last cast boolean mask to ints:

weeks = df.loc[df['Public_Holiday'].eq(1), 'WeekNum']
df['Public_Holiday_Week'] = df['WeekNum'].isin(weeks).astype(int)

print (df)
         Date  WeekNum  Public_Holiday  Public_Holiday_Week
0    1/1/2015        1               1                    1
1    2/1/2015        1               0                    1
2    3/1/2015        1               0                    1
3    4/1/2015        1               0                    1
4    5/1/2015        1               0                    1
5    6/1/2015        1               0                    1
6    7/1/2015        1               0                    1
7    8/1/2015        2               0                    0
8    9/1/2015        2               0                    0
9   10/1/2015        2               0                    0
10  11/1/2015        2               0                    0
11  12/1/2015        2               0                    0
12  13/1/2015        2               0                    0

As pointed @Mohamed Thasin ah if necessary is possible groupby by week, but then get different output, because different week numbers:

df['weeks'] = pd.to_datetime(df['Date'], dayfirst=True).dt.week

weeks = df.loc[df['Public_Holiday'].eq(1), 'weeks']
df['Public_Holiday_Week'] = df['weeks'].isin(weeks).astype(int)
print (df)
         Date  WeekNum  Public_Holiday  weeks  Public_Holiday_Week
0    1/1/2015        1               1      1                    1
1    2/1/2015        1               0      1                    1
2    3/1/2015        1               0      1                    1
3    4/1/2015        1               0      1                    1
4    5/1/2015        1               0      2                    0
5    6/1/2015        1               0      2                    0
6    7/1/2015        1               0      2                    0
7    8/1/2015        2               0      2                    0
8    9/1/2015        2               0      2                    0
9   10/1/2015        2               0      2                    0
10  11/1/2015        2               0      2                    0
11  12/1/2015        2               0      3                    0
12  13/1/2015        2               0      3                    0

Use resample and skip the use of the WeekNum column altogether.

df.assign(
    Public_Holiday_Week=
    df.resample('W-Wed', on='Date').Public_Holiday.transform('max')
)

         Date  WeekNum  Public_Holiday  Public_Holiday_Week
0  2015-01-01        1               1                    1
1  2015-01-02        1               0                    1
2  2015-01-03        1               0                    1
3  2015-01-04        1               0                    1
4  2015-01-05        1               0                    1
5  2015-01-06        1               0                    1
6  2015-01-07        1               0                    1
7  2015-01-08        2               0                    0
8  2015-01-09        2               0                    0
9  2015-01-10        2               0                    0
10 2015-01-11        2               0                    0
11 2015-01-12        2               0                    0
12 2015-01-13        2               0                    0