According to me, the best possible method is to
- Upload both the tables to a database
- create a date and time dimension and have date_id and time_id updated to both the tables.
update the primary key of your business data to the closely related weather data. an Example shown below
Update weather_data set weather_data.id = (SELECT id from business_data where business_data.timestamp_column <= weather_data.timestamp_column ORDER BY business_data.timestamp_column DESC LIMIT 1);
This will get you the business data primary key into weather data which make it easy for you to join.
Good Luck with this one!