Mazzy's Companion Quest - Baldur's Gate 2
Mazzy's Companion Quest begins 7 - 8 days after rescuing her from the Temple Ruins and adding her into your party. You'll also have to complete the Investigate the Deaths in Umar Hills side quest to trigger the messenger that starts this one. It's worth noting that technically Mazzy has 2 Companion Quests, this page is going to cover the quest involving Mazzy's Sister in Trademeet named Save Mazzy's Sister, Pala.
The other quest involving Mazzy starts when you bring her to the front entrance of the Copper Coronet in the Athkatla Slums during the day; it's a short arena quest which takes place inside the Copper Coronet. As for this quest, it begins when you're approached by someone named Danno Fairfoot (pictured above).
Danno will tell your party that Mazzy's sister has gotten sick after drinking a love potion and that Mazzy needs to return home immediately. Mazzy's home is in Trademeet, it should be unlocked on your map for this quest if it isn't already. Alternatively you can also go start Animal Trouble in Trademeet to get the location added to your map as well.
Once in Trademeet look for the Fentan Home location on your map, this is where you can find Mazzy's family and her sister. Inside you'll get some dialogue with Mazzy's family after which you're sent to find a merchant by the name of Wallace. You can find Wallace south of the Fentan Home in the strip of merchants (pictured below). When you get close enough to Wallace dialogue will begin automatically so it won't be hard finding him.
After speaking with Wallace we're sent to the Temple of Waukeen where you'll have to speak with Overgold Renwellyn. If your Reputation or Charisma is low enough you'll have to "donate" 300g to make him search Barl's chambers, after he searches Barl's chambers he'll return to you with proof of your claims.
There will be a scene where Barl is called before you and confronted after which you'll be thrown into a fight with him and the 2 Poison Mist enemies he summons (if he gets a chance to). When the fight ends you'll have another cutscene with Mazzy finding the cure and returning to her home to administer it to her sister.
Eventually Mazzy will ask to leave your party for 24hrs to make sure her sister gets better. It's up to you what you want to do, agreeing to wait for her will make her available as a companion again within 24hrs - refusing to wait will make her unavailable until the Throne of Bhaal.
The choice is yours whether or not you want Mazzy to stick around. Regardless of your choice the quest ends here.