You need () instead []:
arrival_delayed_weather = (flight_data_finalcopy["ArrDelay"] > 0) &
(flight_data_finalcopy["WeatherDelay"]>0)
But it seems you need ix for selecting columns UniqueCarrier and AirlineID by mask - a bit modified boolean indexing:
mask = (flight_data_finalcopy["ArrDelay"] > 0) &
(flight_data_finalcopy["WeatherDelay"]>0)
arrival_delayed_weather_filter=flight_data_finalcopy.ix[mask, ["UniqueCarrier","AirlineID"]]
Sample:
flight_data_finalcopy = pd.DataFrame({'ArrDelay':[0,2,3],
'WeatherDelay':[0,0,6],
'UniqueCarrier':['s','a','w'],
'AirlineID':[1515,3546,5456]})
print (flight_data_finalcopy)
AirlineID ArrDelay UniqueCarrier WeatherDelay
0 1515 0 s 0
1 3546 2 a 0
2 5456 3 w 6
mask = (flight_data_finalcopy["ArrDelay"] > 0) & (flight_data_finalcopy["WeatherDelay"]>0)
print (mask)
0 False
1 False
2 True
dtype: bool
arrival_delayed_weather_filter=flight_data_finalcopy.ix[mask, ["UniqueCarrier","AirlineID"]]
print (arrival_delayed_weather_filter)
UniqueCarrier AirlineID
2 w 5456