Condensate drips constantly when it needs to get rid of excess humidity from the system.. Sometimes it may not drip at all for a while, and sometimes it will drip constantly.
Just sounds like it's doing its job.
The ammount of water your AC produces is related to the ammount it removes from the air. If you've been living there in similar conditions (humidity and temperature) before and it hasn't been this bad it could indicate a number of things. It could be your air filter needs changing or your coil is dirty, both would slow your airflow and let more humidity get sucked out of the air by the AC. It could be a leaky duct or window causing your home to draw in outside air. It could also be an indication of undercharge in your unit. If your coil freezes up with proper airflow then you will know its an undercharge. If you are really concerned start checking for proper airflow and leaks.