All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If your parents commanded you to refrain from observing voluntary fasting because it harms you in their opinion, then you are obliged to obey them; since obeying them takes precedence over voluntary fasting. The Fatwa of the Permanent Committee for Iftaa’ reads: "What is the ruling on observing voluntary fasting without the parents’ consent?" The answer was: "Obedience to one’s parents is obligatory, and voluntary fasting is a recommended act. So, if your parents ordered you to give up voluntary fasting, it is obligatory on you to obey them." [End of Quote] Moreover, Shaykh Ibn Baaz was asked: "What about a person whose mother forbids him from observing voluntary fasting, and she says to him: ‘You have fasted a lot, and this is enough.’ Should I fast or give up voluntary fast, noting that my body is weak and I cannot endure fasting?" He replied: “You have to obey your mother because she is kind and compassionate towards you, and keen on your best interest. It is incumbent on you to listen to your mother and obey her regarding what she tells you about the voluntary fast." [End of Quote]
You can please your parents by showing kindness to them and observing less voluntary fasting. You can settle for fasting on Mondays, Thursdays, the Three White Days (i.e. the 13th, 14th and 15th of each lunar month), and the like in order for you to follow the Sunnah. By doing so, you would be doing good, Allah willing.
Allah Knows best.